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oskar 883daa8600 MacBook-Pro-de-Oscar.local 2026-6-12:0:42:54 2026-06-12 00:42:54 +02:00
oskar ee01f694d1 MacBook-Pro-de-Oscar.local 2026-6-11:18:42:53 2026-06-11 18:42:54 +02:00
oskar 8024ed17b4 MacBook-Pro-de-Oscar.local 2026-6-11:0:35:19 2026-06-11 00:35:19 +02:00
oskar 5141bf6508 MacBook-Pro-de-Oscar.local 2026-6-10:19:27:55 2026-06-10 19:27:55 +02:00
oskar af7dc45db0 MacBook-Pro-de-Oscar.local 2026-6-10:17:27:54 2026-06-10 17:27:54 +02:00
oskar bc15c851be MacBook-Pro-de-Oscar.local 2026-6-10:15:27:54 2026-06-10 15:27:54 +02:00
oskar a05fadfc75 MacBook-Pro-de-Oscar.local 2026-6-10:3:16:12 2026-06-10 03:16:13 +02:00
oskar 779cfecf28 MacBook-Pro-de-Oscar.local 2026-6-9:1:48:5 2026-06-09 01:48:05 +02:00
oskar 2e3ad73faf MacBook-Pro-de-Oscar.local 2026-6-8:21:48:4 2026-06-08 21:48:04 +02:00
oskar 3040f5c7ea MacBook-Pro-de-Oscar.local 2026-6-8:1:51:52 2026-06-08 01:51:52 +02:00
oskar 2d1a43d447 MacBook-Pro-de-Oscar.local 2026-6-8:0:51:52 2026-06-08 00:51:52 +02:00
oskar 308b7ba5d3 MacBook-Pro-de-Oscar.local 2026-6-7:22:51:52 2026-06-07 22:51:52 +02:00
oskar c4ce611a63 MacBook-Pro-de-Oscar.local 2026-6-7:20:51:52 2026-06-07 20:51:52 +02:00
oskar 3079b4854c MacBookPro.lan 2026-6-6:23:23:47 2026-06-06 23:23:47 +02:00
oskar f575ec76ff MacBookPro.lan 2026-6-6:22:23:47 2026-06-06 22:23:47 +02:00
oskar ab29549a71 MacBookPro.lan 2026-6-6:21:23:47 2026-06-06 21:23:47 +02:00
oskar 15f4b20152 MacBookPro.lan 2026-6-6:20:23:47 2026-06-06 20:23:47 +02:00
oskar 3f088fc13d MacBookPro.lan 2026-6-6:19:23:47 2026-06-06 19:23:47 +02:00
oskar 6337e0e32e MacBookPro.lan 2026-6-5:18:2:16 2026-06-05 18:02:16 +02:00
oskar 17d6cff644 MacBookPro.lan 2026-6-5:1:5:57 2026-06-05 01:05:58 +02:00
oskar 3926ea5536 MacBookPro.lan 2026-6-4:18:34:1 2026-06-04 18:34:01 +02:00
oskar c36ea200bb MacBook-Pro-de-Oscar.local 2026-6-3:22:7:20 2026-06-03 22:07:20 +02:00
oskar aa3f49c476 MacBook-Pro-de-Oscar.local 2026-6-3:18:37:44 2026-06-03 18:37:45 +02:00
oskar 1f889a4459 MacBook-Pro-de-Oscar.local 2026-6-3:3:10:33 2026-06-03 03:10:34 +02:00
oskar 937bef48f5 MacBook-Pro-de-Oscar.local 2026-6-3:2:10:34 2026-06-03 02:10:34 +02:00
oskar c1dfba0c57 MacBookPro.lan 2026-5-31:20:45:58 2026-05-31 20:45:59 +02:00
oskar 2608232f5b MacBookPro.lan 2026-5-31:19:45:55 2026-05-31 19:45:55 +02:00
oskar f3252e2341 MacBookPro.lan 2026-5-31:18:45:55 2026-05-31 18:45:55 +02:00
oskar d7291bd730 MacBookPro.lan 2026-5-31:17:45:55 2026-05-31 17:45:55 +02:00
oskar 285872340f MacBookPro.lan 2026-5-31:16:45:55 2026-05-31 16:45:55 +02:00
oskar 12797b14e9 MacBookPro.lan 2026-5-31:15:45:55 2026-05-31 15:45:55 +02:00
oskar 3110cf066a MacBookPro.lan 2026-5-31:14:45:55 2026-05-31 14:45:55 +02:00
oskar 7e26ea4279 MacBookPro.lan 2026-5-30:15:15:45 2026-05-30 15:15:45 +02:00
oskar 9f0e6503ba MacBookPro.lan 2026-5-29:22:59:30 2026-05-29 22:59:31 +02:00
oskar 93e929944d MacBookPro.lan 2026-5-29:20:58:21 2026-05-29 20:58:22 +02:00
oskar 3cbc984e09 MacBookPro.lan 2026-5-29:2:4:41 2026-05-29 02:04:41 +02:00
oskar 0ac1f1f485 MacBookPro.lan 2026-5-29:0:4:41 2026-05-29 00:04:41 +02:00
oskar 438c9f3fda macbook-pro-de-oscar.home 2026-5-26:19:19:34 2026-05-26 19:19:34 +02:00
oskar 7c69be107e MacBook-Pro-de-Oscar.local 2026-5-26:14:22:40 2026-05-26 14:22:41 +02:00
oskar 9ffe120f6a macbook-pro-de-oscar.home 2026-5-26:1:15:26 2026-05-26 01:15:27 +02:00
oskar 4caab595f9 macbook-pro-de-oscar.home 2026-5-25:23:12:53 2026-05-25 23:12:53 +02:00
oskar 52958e3686 macbook-pro-de-oscar.home 2026-5-25:1:39:30 2026-05-25 01:39:30 +02:00
oskar f1e92ddc00 MacBookPro.lan 2026-5-23:1:36:13 2026-05-23 01:36:14 +02:00
oskar 6aaebdd087 MacBook-Pro-de-Oscar.local 2026-5-22:19:27:20 2026-05-22 19:27:20 +02:00
oskar 3a0ce78d8a MacBook-Pro-de-Oscar.local 2026-5-19:13:51:57 2026-05-19 13:51:58 +02:00
oskar 312f88aa8d MacBook-Pro-de-Oscar.local 2026-5-19:12:51:57 2026-05-19 12:51:58 +02:00
oskar 1dbdcee53f MacBook-Pro-de-Oscar.local 2026-5-19:3:22:36 2026-05-19 03:22:36 +02:00
oskar ed213a90a6 MacBookPro.lan 2026-5-18:15:20:17 2026-05-18 15:20:18 +02:00
oskar f21976b7e6 MacBookPro.lan 2026-5-17:21:2:23 2026-05-17 21:02:24 +02:00
oskar f9bd96356a MacBook-Pro-de-Oscar.local 2026-5-16:20:35:13 2026-05-16 20:35:13 +02:00
oskar 54834ec30a MacBook-Pro-de-Oscar.local 2026-5-14:19:1:12 2026-05-14 19:01:14 +02:00
oskar 54cdfe8332 device-92.home 2026-5-13:1:15:2 2026-05-13 01:15:02 +02:00
oskar 052d9d120c MacBookPro.lan 2026-5-12:14:31:57 2026-05-12 14:31:57 +02:00
oskar dc00832b1d MacBookPro.lan 2026-5-11:12:42:57 2026-05-11 12:42:57 +02:00
89 changed files with 3982 additions and 5050 deletions
Vendored
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"name": "BRAT",
"version": "2.0.4",
"version": "2.0.8",
"minAppVersion": "1.11.4",
"description": "Easily install a beta version of a plugin for testing.",
"description": "Easily install plugin beta versions for testing.",
"author": "TfTHacker",
"authorUrl": "https://github.com/TfTHacker/obsidian42-brat",
"authorUrl": "https://github.com/TfTHacker",
"helpUrl": "https://tfthacker.com/BRAT",
"isDesktopOnly": false,
"fundingUrl": {
+32 -2
View File
@@ -111,12 +111,12 @@
/* Hide filtered plugin items */
.brat-plugin-item[hidden] {
display: none !important;
display: none;
}
/* Hide filtered theme items */
.brat-theme-item[hidden] {
display: none !important;
display: none;
}
/* Filter and button layout */
@@ -150,3 +150,33 @@
.brat-filter-and-button .setting-item-control {
justify-content: flex-end;
}
.brat-full-width-input {
width: 100%;
}
.brat-modal-divider {
border-top: 1px solid var(--background-modifier-border);
margin-top: 30px;
}
.brat-credits {
font-style: italic;
}
.brat-promotional-links {
float: right;
}
.brat-promotional-links-modal {
padding: 10px 15px;
}
.brat-promotional-links-settings {
padding: 15px;
margin-left: 15px;
}
.brat-promotional-links-coffee {
padding-left: 10px;
}
+3 -1
View File
@@ -100,6 +100,8 @@
"date-birth": "date",
"date-death": "date",
"excerpt_of": "multitext",
"part": "multitext"
"part": "multitext",
"BC-tag-note-sibling-field": "text",
"BC-traverse-note-field": "text"
}
}
@@ -7,7 +7,9 @@ tags: [excalidraw]
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
# Excalidraw Data
## Text Elements
Reset ^RoHLK7dp
Set ^NORclDsY
@@ -15,662 +17,54 @@ Set ^NORclDsY
Sense ^1Hgsf293
%%
# Drawing
```json
{
"type": "excalidraw",
"version": 2,
"source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.0.16",
"elements": [
{
"id": "M3sG8YHxZ9sgeIVjjEQLA",
"type": "ellipse",
"x": -85.12890625,
"y": -261.17578125,
"width": 126.60546875,
"height": 197.8984375,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": {
"type": 2
},
"seed": 993107708,
"version": 156,
"versionNonce": 1305930308,
"isDeleted": false,
"boundElements": [
{
"id": "ZYIT0c9oGbNc5aehe-1SY",
"type": "arrow"
},
{
"id": "Ut1skK0QDvebF6_jIOg2G",
"type": "arrow"
}
],
"updated": 1707955502767,
"link": null,
"locked": false
},
{
"id": "rYTrBs1w9j1SpRu51PUHS",
"type": "line",
"x": 30,
"y": -231.359375,
"width": 71.591796875,
"height": 26.908203125,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 1842072388,
"version": 154,
"versionNonce": 211812860,
"isDeleted": false,
"boundElements": null,
"updated": 1707955441542,
"link": null,
"locked": false,
"points": [
[
0,
0
],
[
44.68359375,
0
],
[
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-26.908203125
]
],
"lastCommittedPoint": [
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-26.908203125
],
"startBinding": null,
"endBinding": null,
"startArrowhead": null,
"endArrowhead": null
},
{
"id": "RoHLK7dp",
"type": "text",
"x": -193.41796875,
"y": -300.7421875,
"width": 57.599945068359375,
"height": 25,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 819643516,
"version": 69,
"versionNonce": 642532292,
"isDeleted": false,
"boundElements": [
{
"id": "BpGvrmBpa8qqpkuxhhofa",
"type": "arrow"
}
],
"updated": 1707955428464,
"link": null,
"locked": false,
"text": "Reset",
"rawText": "Reset",
"fontSize": 20,
"fontFamily": 1,
"textAlign": "left",
"verticalAlign": "top",
"baseline": 18,
"containerId": null,
"originalText": "Reset",
"lineHeight": 1.25
},
{
"id": "BpGvrmBpa8qqpkuxhhofa",
"type": "arrow",
"x": -144.28125,
"y": -259.96484375,
"width": 152.21875,
"height": 28.537109375,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 759511292,
"version": 133,
"versionNonce": 1349727684,
"isDeleted": false,
"boundElements": null,
"updated": 1707955439251,
"link": null,
"locked": false,
"points": [
[
0,
0
],
[
28.537109375000014,
28.537109375
],
[
152.21875,
28.537109375
]
],
"lastCommittedPoint": [
152.21875,
28.537109375
],
"startBinding": {
"elementId": "RoHLK7dp",
"focus": 0.19226641198388442,
"gap": 15.77734375
},
"endBinding": null,
"startArrowhead": "arrow",
"endArrowhead": null
},
{
"id": "jT8cpDxp-r2QKdnlSbfIo",
"type": "line",
"x": -172.37890625,
"y": -229.9765625,
"width": 195.75390625,
"height": 28.3984375,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 1414312700,
"version": 136,
"versionNonce": 1363863492,
"isDeleted": false,
"boundElements": null,
"updated": 1707955450248,
"link": null,
"locked": false,
"points": [
[
0,
0
],
[
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28.3984375
],
[
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28.3984375
]
],
"lastCommittedPoint": [
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28.3984375
],
"startBinding": null,
"endBinding": null,
"startArrowhead": null,
"endArrowhead": null
},
{
"id": "ZYIT0c9oGbNc5aehe-1SY",
"type": "arrow",
"x": 46.71484375,
"y": -201.4765625,
"width": 72.607421875,
"height": 30.279296875,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 1179727612,
"version": 129,
"versionNonce": 915842500,
"isDeleted": false,
"boundElements": null,
"updated": 1707955470759,
"link": null,
"locked": false,
"points": [
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],
[
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],
[
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],
"lastCommittedPoint": [
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"startBinding": {
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"focus": -0.39666811416841025,
"gap": 10.081109002050752
},
"endBinding": null,
"startArrowhead": null,
"endArrowhead": "arrow"
},
{
"id": "NORclDsY",
"type": "text",
"x": -201.171875,
"y": -256.671875,
"width": 34.39996337890625,
"height": 25,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 679451004,
"version": 58,
"versionNonce": 883398396,
"isDeleted": false,
"boundElements": null,
"updated": 1707955477526,
"link": null,
"locked": false,
"text": "Set",
"rawText": "Set",
"fontSize": 20,
"fontFamily": 1,
"textAlign": "left",
"verticalAlign": "top",
"baseline": 18,
"containerId": null,
"originalText": "Set",
"lineHeight": 1.25
},
{
"id": "1Hgsf293",
"type": "text",
"x": -218,
"y": -71.12109375,
"width": 54.23994445800781,
"height": 25,
"angle": 0,
"strokeColor": "#1e1e1e",
"backgroundColor": "transparent",
"fillStyle": "solid",
"strokeWidth": 2,
"strokeStyle": "solid",
"roughness": 1,
"opacity": 100,
"groupIds": [],
"frameId": null,
"roundness": null,
"seed": 503883900,
"version": 6,
"versionNonce": 1649959620,
"isDeleted": false,
"boundElements": null,
"updated": 1707955483329,
"link": null,
"locked": false,
"text": "Sense",
"rawText": "Sense",
"fontSize": 20,
"fontFamily": 1,
"textAlign": "left",
"verticalAlign": "top",
"baseline": 18,
"containerId": null,
"originalText": "Sense",
"lineHeight": 1.25
},
{
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"type": "line",
"x": -185.4609375,
"y": -75.3359375,
"width": 205.71484375,
"height": 51.369140625000014,
"angle": 0,
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},
{
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"y": -127.328125,
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},
{
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},
{
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},
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"isDeleted": true,
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"points": [
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],
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},
{
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"y": -271.875,
"width": 164.00390625,
"height": 34.048828125,
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],
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}
],
"appState": {
"theme": "dark",
"viewBackgroundColor": "#ffffff",
"currentItemStrokeColor": "#1e1e1e",
"currentItemBackgroundColor": "transparent",
"currentItemFillStyle": "solid",
"currentItemStrokeWidth": 2,
"currentItemStrokeStyle": "solid",
"currentItemRoughness": 1,
"currentItemOpacity": 100,
"currentItemFontFamily": 1,
"currentItemFontSize": 20,
"currentItemTextAlign": "left",
"currentItemStartArrowhead": null,
"currentItemEndArrowhead": "arrow",
"scrollX": 495.3359375,
"scrollY": 410.21484375,
"zoom": {
"value": 1
},
"currentItemRoundness": "sharp",
"gridSize": null,
"gridColor": {
"Bold": "#C9C9C9FF",
"Regular": "#EDEDEDFF"
},
"currentStrokeOptions": null,
"previousGridSize": null,
"frameRendering": {
"enabled": true,
"clip": true,
"name": true,
"outline": true
}
},
"files": {}
}
## Drawing
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K0J0N0H0EMKMJMDMJek/pPm/sNlrCWj/tweIqjL9O7LsANeARBrHKLe4fAYDr9kFdbQ7YFT+MVSBDWViB0BFRWQQSjj3OANdFiHAHAMqF4mLZ+E+BkOULRKQHxOsAwIQAgBQGZLLvNbiRAHSDKNnTnayBANgCIJAr0DOPoMqO/JNXeQnQXb+ENMXekKndienU+YteoXndXUXSXchKtSSetf+fnYXbXSXWXVtaglXQPUekPeKmtXSX3e3YPekEPP5
rKuYf3TXRPekFhMFtYdVKvR3ekMhCUp6RUmPWvVAHXfoAfVkLUYUjvXPevfoKkn6RIE0i0rvfPaXfbYgddZAHfWfSXSMADl/UVc4ifXvfoIDiePQUAm3ePX/fvTQkPFaM4VqNgMSAqM2UaKiHVX9WtlDCg2g/gO+IFK8EvJWKimJSUEYGwAYBHdDAQGckaKjiUL/efYva4aGFqIpKQGGSUNyCQNfW6QUOQoscQMqAgJPCEQnXw8QBUJLQA7gJoME
CqUI9IxLvpGZFSAPKQMoOyAABR7y5ah6GMGPUCoCf4ACUmo8SygiYEo5Q2jejLE+IvAgeLjzjFj9ZQjv9w9ZIm97SnAoYyD0W8SMkix7l+kmQCjSj3AxxkxKwMTJZJxEAyx0dxZpZB0ByQyaTST+gEoZIpAXYDuCT6TWYuTcdTA8jij30xxTDcymggwCA2A2QioyxcAsjDylT0T+RsRWITThAjAJ41D+AtDhE3xgyjT/jXAkxQghIBgkDvGrFJp3
T1CBgxRwQfTSOFFkalsUwfTAzQzkctTEAjgzAUTH8WQKkFQmQQgyNM1TlLkgQMoTAmQIeGAyxVTiC0eW+nT1TiTCd44FQJAXFLTuAIdCcPzhksTQjy4mAazEzzY7T34MZ0kLiukmh4Qq6bi+YQAA
```
%%
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-1
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tags:
aliases:
---
![[attachments/Pasted image 20260508182131.png]]
-2
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aliases:
---
-
- ? cacher le dossier attachments
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---
up:
- "[[filtre engendré]]"
tags:
- s/maths/logique
aliases:
---
> [!definition] [[base de filtre]]
> Soit $X$ un ensemble infini.
> Soit $\mathcal{B}\subseteq \mathcal{P}(X)$ une partie de $\mathcal{P}(X)$
> $\mathcal{B}$ est une **base de filtre** sur $X$ si :
> - $\emptyset \notin \mathcal{B}$
> - $\mathcal{B}$ est stable par intersection : $\forall A, B \in \mathcal{B},\quad A \cap B \in \mathcal{B}$
^definition
# Propriétés
# Exemples
+1 -1
Submodule blog updated: 1d1998c79e...6620c6afb8
+16
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@@ -0,0 +1,16 @@
---
up:
- "[[logique]]"
tags:
- s/maths/logique
aliases:
---
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
+7 -7
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@@ -1,12 +1,12 @@
---
id: classifier et diviser les personnes
aliases: []
tags: []
alias:
- classifier les personnes
up: "[[étapes d'un génocide]]"
tags:
- "#s/science/histoire"
- "#s/philosophie"
- "#s/science/zetetique"
aliases:
- "classifier les personnes"
---
up:: [[étapes d'un génocide]]
#s/science/histoire #s/philosophie #s/science/zetetique
Classifier les gens, par *race*, par croyances, physique...
+1 -1
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@@ -2,6 +2,6 @@
---
Dans l'[[logique approche sémantique]], une [[théorie logique]] est _consistante_ (ou encore [[satisfaisable]]) ssi elle possède au moins un [[modèle]]. Dans le cas contraire, la théorie est dire inconsistante.
Dans l'[[logique approche sémantique]], une [[théorie logique]] est _consistante_ (ou encore [[satisfaisable]]) ssi elle possède au moins un [[théorie des modèles . modèle]]. Dans le cas contraire, la théorie est dire inconsistante.
Une théorie inconsistante est considérée comme de peu d'intérêt
+5
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---
up:
tags:
aliases:
---
+1 -1
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@@ -2,7 +2,7 @@
---
Une [[proposition]] $B$ est la _conséquence sémantique_ d'une [[proposition]] $A$ ssi **tout [[modèle]] de $A$ est un [[modèle]] de $B$**.
Une [[proposition]] $B$ est la _conséquence sémantique_ d'une [[proposition]] $A$ ssi **tout [[théorie des modèles . modèle]] de $A$ est un [[théorie des modèles . modèle]] de $B$**.
# Définition
$A\models B \iff \forall x, x\models A \implies x\models B$
+1 -1
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@@ -1,7 +1,7 @@
#s/maths/logique
---
Une contradiction est une [[proposition]] qui n'admet **aucun [[modèle]]**.
Une contradiction est une [[proposition]] qui n'admet **aucun [[théorie des modèles . modèle]]**.
C'est-à-dire qu'elle n'est vraie pour aucune [[interprétation]].
On dit aussi que cette proposition est _insatifaisable_
+2 -2
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@@ -1,8 +1,8 @@
# Todo
- [ ] #task trouver pompe à vélo
- [ ] #task acheter billet de train 🔺
- [ ] #task mail prof de computational semantics
- [x] #task acheter billet de train 🔺 ✅ 2026-05-31
- [x] #task mail prof de computational semantics ✅ 2026-05-31
- [ ] possible de suivre le cours maintenant ?
- [ ] question sur le lab 1 (is my solution too hacky ?)
+20
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# Todo
```tasks
due 2026-05-31
not done
```
# I did
> [!smallquery]- Modified files
> ```dataview
> LIST file.mtime
> where file.mtime > date(this.file.name) and file.mtime < (date(this.file.name) + dur(1 day)) sort file.mtime asc
> ```
```tasks
done 2026-05-31
short mode
```
# I am gratefull to
+1 -1
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@@ -3,4 +3,4 @@
---
Une _démonstration formelle_ est l'application successive de plusieurs [[règle d'inférence|règles d'inférence]] à partir d'un ensemble [[axiome|d'axiomes]] ou de [[théorème|théorèmes]] déjà démontrés.
Une Démonstration produit systématiquement de nouveaux théorèmes qui sont la [[conséquence formelle]]
Une Démonstration produit systématiquement de nouveaux théorèmes qui sont la [[conséquence]]
+18
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@@ -0,0 +1,18 @@
---
up:
- "[[calcul propositionnel]]"
tags:
- s/maths/logique
- o
aliases:
- contradictoire
---
> [!definition] [[ensemble de formules contradictoire]]
> Un ensemble de formules $\mathscr{A}$ est **contradictoire** si et seulement si il n'est pas [[ensemble de formules satisfaisable|satisfaisable]]
^definition
# Propriétés
# Exemples
+14
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@@ -0,0 +1,14 @@
---
up:
- "[[formule logique|formules logiques]]"
tags:
- s/maths/logique
aliases:
- satisfaisable
---
> [!definition] Définition
> Soit $\mathscr{A}$ un ensemble de formules du [[calcul propositionnel]]
> $\mathscr{A}$ est **satisfaisable** (ou **consistant**, ou **non contradictoire**) si et seulement s'il existe au moins une [[valuation]] qui satisfait $\mathscr{A}$
^definition
+21
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@@ -0,0 +1,21 @@
---
up:
- "[[calcul propositionnel]]"
tags:
- s/maths/logique
aliases:
- satisfait
---
> [!definition] [[ensemble de formules satisfait]]
> Soit $\mathscr{A}$ un ensemble de formules du [[calcul propositionnel]] sur l'ensemble de variables propositionnelles $P$
> Soit $\delta$ une [[valuation d'une formule logique|valuation]] sur $P$
> On dit que $\mathscr{A}$ est **satisfait** par $\delta$ si et seulempent si $\delta$ satisfait toutes les formules qui appartiennent à $\mathscr{A}$ :
> $\boxed{\forall F \in \mathscr{A},\quad \delta(F) = 1}$
^definition
# Propriétés
# Exemples
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@@ -1,12 +0,0 @@
---
up:
- "[[formule logique|formules logiques]]"
tags:
- s/maths/logique
aliases:
---
> [!definition] Définition
> Soit $\mathcal{F}$ l'ensemble des formules propositionnelles
^definition
+10 -3
View File
@@ -6,9 +6,16 @@ tags:
aliases:
- ensembles
---
> [!definition] Définition
>
^definition
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
# Propriétés
@@ -0,0 +1,12 @@
---
up:
- "[[calcul propositionnel]]"
tags:
- s/maths/logique
aliases:
- équivalents
---
> [!definition] [[ensembles de formules logiquement équivalents]]
> Deux ensembles de formules $\mathscr{A}$ et $\mathscr{B}$ sont **équivalents** si et seulement si toute formule de $\mathscr{A}$ est conséquence de $\mathscr{B}$
^definition
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@@ -78,7 +78,7 @@ views:
- property: watchlist
direction: DESC
columnSize:
file.name: 352
file.name: 431
note.scoreImdb: 47
note.director: 141
note.year: 64
+12 -10
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@@ -6,17 +6,19 @@ tags:
aliases:
---
> [!definition] Définition
> On définit $\mathscr{F}$ le filtre de Fréchet par :
> [!definition] [[filtre de fréchet]]
> Soit $X$ un ensemble infini.
> On définit $\mathscr{F}$ le [[filtre]] de Fréchet par :
> $A \in \mathscr{F}$ si $X - A$ est fini
> - i on pourra le noter $\mathscr{F}_{\mathrm{cof}}$
>
> > [!démonstration]- Démonstration que c'est bien un filtre
> > 1. $X - X = \emptyset$ est bien fini
> > 2. soient $A, B \in \mathscr{F}$ on a :
> > $X - (A \cap B) = (X-A) \cup (X-B)$
> > or la réunion de deux ensembles finis est finie d'où il suit que $A \cap B \in \mathscr{F}$
> > 3. Soit $A \in \mathscr{F}$ avec $A \subseteq B$
> > $X - B \subseteq X - A$ or on sait que $X - A$ est fini, et qu'une partie d'un ensemble fini est finie, d'où on a que $X - B$ est fini et donc que $B \in \mathscr{F}$
^definition
# Démonstration que c'est bien un filtre
1. $X - X = \emptyset$ est bien fini
2. soient $A, B \in \mathscr{F}$ on a :
$X - (A \cap B) = (X-A) \cup (X-B)$
or la réunion de deux ensembles finis est finie d'où il suit que $A \cap B \in \mathscr{F}$
3. Soit $A \in \mathscr{F}$ avec $A \subseteq B$
$X - B \subseteq X - A$ or on sait que $X - A$ est fini, et qu'une partie d'un ensemble fini est finie, d'où on a que $X - B$ est fini et donc que $B \in \mathscr{F}$
+21
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@@ -0,0 +1,21 @@
---
up:
- "[[filtre]]"
tags:
- s/maths/logique
aliases:
---
> [!definition] [[filtre engendré]]
> Soit $\mathcal{B}$ une [[base de filtre]] sur $X$
> Le **filtre engendré** par $\mathcal{B}$ est le [[filtre]] $\mathscr{F}_{\mathcal{B}}$ défini par :
> $\boxed{\mathscr{F}_{\mathcal{B}} = \{ F \in \mathcal{P}(X) \mid \exists B \in \mathcal{B},\quad B \subseteq F \}}$
>
> > [!démonstration]- Démonstration : $\mathscr{F}_{\mathcal{B}}$ est bien un filtre
> >
^definition
# Propriétés
# Exemples
+2 -2
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@@ -2,10 +2,10 @@
id: firefox troubleshooot
aliases: []
tags:
- #t/troubleshoot
-
up:
- "[[firefox]]"
- "[[firefox troubleshooot]]"
- "[[troubleshoot]]"
---
```breadcrumbs
@@ -0,0 +1,30 @@
---
up:
- "[[calcul propositionnel]]"
tags:
- s/maths/logique
aliases:
- conséquence
- ⊢*
---
> [!definition] [[formule conséquence d'un ensemble de formules]]
> Soit $\mathscr{A}$ un ensembles de formules et $G$ une formule du [[calcul propositionnel]]
> $G$ est **conséquence** de $\mathscr{A}$ si et seulement si toute distribution de valeurs de vérité qui satisfait $\mathscr{A}$
^definition
# Propriétés
> [!proposition]+
> $\mathscr{A} \vdash^{*} G \iff \mathscr{A} \cup \{ \neg G \}$ est [[ensemble de formules contradictoire|contradictoire]]
> > [!démonstration]- Démonstration
> > - $\boxed{\implies}$ supposons que $\mathscr{A} \vdash^{*} G$
> > Soit $\delta$ une [[valuation]] qui [[ensemble de formules satisfait|satisfait]] $\mathscr{A}$, i.e. $\forall F \in \mathscr{A},\quad \delta(F) = 1$
> > Puisque l'on a supposé $\mathscr{A} \vdash^{*} G$ sait que $\delta(G)=1$, et donc que $\delta(\neg G) = 0$, ce qui montre bien qu'aucune valuation satisfaisant $\mathscr{A}$ ne peut satisfaire aussi $\neg G$, et donc que $\mathscr{A} \cup \{ \neg G \}$ est contradictoire
> > - $\boxed{\impliedby}$ supposons que $\mathscr{A} \cup \{ \neg G \}$ est contradictoire
> > Alors, on sait que pour toute valuation $\delta$ on a $\exists F \in \mathscr{A} \cup \{ \neg G \},\quad \delta (F) = 0$
> > -
# Exemples
+1
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@@ -4,6 +4,7 @@ up:
tags:
- s/maths/logique
aliases:
- formule close
---
> [!definition] Définition
+1 -1
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@@ -42,4 +42,4 @@ critiqué par :
## Obstacle logico-mathématique
[[paradoxe de Russel]]
[[paradoxe de Russell]]
@@ -0,0 +1,7 @@
# Changing installation settings
You can edit settings for a certain app using :
`brew edit <name>`
That opens a configuration file that controls taht installation settings.
Then, you can recompile that app using :
`brew reinstall --build-from-source <name>`
+13
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@@ -0,0 +1,13 @@
---
up:
- "[[homebrew]]"
tags:
- "#s/informatique"
aliases:
- clear homebrew cache
---
```sh
homebrew cleanup --prune=all
```
@@ -1,10 +1,9 @@
---
alias: [ "homebrew désinstaller avec les dépendances" ]
---
up:: [[homebrew]]
title:: "`brew uninstall <package> && brew autoremove`"
#s/informatique
up: "[[homebrew]]"
tags:
- "#s/informatique"
aliases:
- homebrew désinstaller avec les dépendances
---
Pour désinstaller un package
+13 -11
View File
@@ -1,13 +1,15 @@
up::[[installing things]]
title::"macos package manager"
#s/informatique
---
up: "[[installing things]]"
tags:
- "#s/informatique"
---
----
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
# Changing installation settings
You can edit settings for a certain app using :
`brew edit <name>`
That opens a configuration file that controls taht installation settings.
Then, you can recompile that app using :
`brew reinstall --build-from-source <name>`
+1 -1
View File
@@ -11,5 +11,5 @@ tags: []
> collapse: true
> show-attributes: [field]
> field-groups: [downs]
> depth: [0, 0]
> depth: [0, 2]
> ```
@@ -0,0 +1,7 @@
---
aliases:
- langage
-
up:
tags:
---
+21
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@@ -0,0 +1,21 @@
---
up:
- "[[ligne de commande]]"
- "[[système d'exploitation]]"
tags:
- s/informatique
aliases:
---
Outil qui gère des daemons.
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
+16
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@@ -0,0 +1,16 @@
---
up:
tags:
aliases:
---
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
remplace [[cron]] sur macos : permet de schedule des tâches.
+2 -2
View File
@@ -11,6 +11,6 @@ $$\begin{array}{|r|l|}
\left.\displaystyle\lim_{x\rightarrow+\infty} \dfrac{e^x}{x^\alpha}\right|_{\alpha>0} & +\infty \\\hline
\displaystyle\lim_{x\rightarrow+\infty} & \\\hline
\left.\displaystyle\lim_{x\rightarrow+\infty} \dfrac{(\ln (x))^{\alpha}}{x^\beta}\right|_{\beta>0} & 0 \\\hline
\disp\lim_{x\rightarrow 0} \dfrac{\sin x}x & 1\\\hline
\disp\lim_{x\rightarrow 0} \dfrac{1 - \cos(x)}{x^2} & \dfrac12 \\\hline
\displaystyle \lim_{x\rightarrow 0} \dfrac{\sin x}x & 1\\\hline
\displaystyle \lim_{x\rightarrow 0} \dfrac{1 - \cos(x)}{x^2} & \dfrac12 \\\hline
\end{array}$$
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@@ -0,0 +1,28 @@
---
up:
- "[[terminal commandes]]"
- "[[launchd]]"
tags:
- s/informatique
aliases:
---
Wrapper autour de `lauchctl` pour configurer plus aisément [[launchd]].
- gh https://github.com/sosedoff/lunchy-go
- source:: [[sosedofflunchy-go OSX Launch Manager]]
# Installation
`brew install lunchy-go`
# Cheat sheet
`lunchy ...`
- `ls` [pattern]
- `start` [pattern]
- `stop` [pattern]
- `restart` [pattern]
- `status`, `ps` [pattern]
- `install` [file]
- `show` [pattern]
- `edit` [pattern]
- `remove`, `rm` [pattern]
- `scan` [path]
+10
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@@ -0,0 +1,10 @@
---
up:
- "[[troubleshoot]]"
- "[[macos]]"
tags:
- "#s/informatique"
aliases:
---
problème : beaucoup de place perdue dans "system data"
-9
View File
@@ -1,9 +0,0 @@
#s/maths/logique
----
Un modèle logique est **une [[interprétation]] particulière d'une [[proposition]]**.
On dit qu'une interprétation $I$ est un [[modèle]] d'une [[proposition]] logique $\Phi$ ssi $I(\Phi) = \mathbb{V}$.
Si toutes les interprétations de $P$ sont aussi des modèles de $P$, alors on dit que $P$ est une [[tautologie]].
+237 -239
View File
@@ -292,480 +292,478 @@ e9894d7bda60af851e0fb13a19aa0e8095919e3e: [[attachments/Pasted Image 20260221211
## Drawing
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@@ -21,4 +21,6 @@ up:: [[politique]], [[psychologie]], [[sociologie]]
- projectivité
- projection à l'extérieur de pulsions émotionnelles intérieures
- sexe
- intérêt exagéré pour les "affaires sexuelles"
- intérêt exagéré pour les "affaires sexuelles"
+63 -63
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@@ -2,84 +2,84 @@
# Claire
> - j'ai un truc qui bloque le levier de vitesse
> - ça s'appelle du maquillage !
- j'ai un truc qui bloque le levier de vitesse
- ça s'appelle du maquillage !
> - Ah, c'est pas toi qui est sous la douche !
> - ah bon ?
- Ah, c'est pas toi qui est sous la douche !
- ah bon ?
- je suis malade, j'ai du mal à ne plus l'être
- je suis malade, j'ai du mal à ne plus l'être
# Oscar
- "Dans mon contrôle de maths, pour avoir $20$, il fallait avoir $0$"
- Tu as entendu, Oscar ? Gérard a dit que tu avais des parents intelligents ! Et Oscar de répondre : « sil a fallu quelquun daussi intelligent que lui pour le remarquer, cest que c’était pas facile à voir ! »
- "qui à fait l'appel du 18 juin ? Je sait pas, mais il devait pas être bien après 18 joints"
- "il à perdu sa clef !", "bah non, c'est à Paris, Saclay !"
- c'est pas parce que tu vas plus vite que le son que tu est dans le silence
- "Dans mon contrôle de maths, pour avoir $20$, il fallait avoir $0$"
- Tu as entendu, Oscar ? Gérard a dit que tu avais des parents intelligents ! Et Oscar de répondre : « sil a fallu quelquun daussi intelligent que lui pour le remarquer, cest que c’était pas facile à voir ! »
- "qui à fait l'appel du 18 juin ? Je sait pas, mais il devait pas être bien après 18 joints"
- "il à perdu sa clef !", "bah non, c'est à Paris, Saclay !"
- c'est pas parce que tu vas plus vite que le son que tu est dans le silence
# Clara
- Je me pose des questions sur pourquoi les gens sont si stupides
- Je me pose des questions sur pourquoi les gens sont si stupides
# Samuel
- Pourquoi les plongeurs basculent en arrière ? Parce que si ils basculent en avant, ils tombent dans le bateau.
- Pourquoi les plongeurs basculent en arrière ? Parce que si ils basculent en avant, ils tombent dans le bateau.
# Jean Claude
- "Le dimanche il pleut plus souvent à l'extérieur"
- "Le dimanche il pleut plus souvent à l'extérieur"
# Gérard
- "Le 3$^{\text{ème}}$ degré est un premier non avoué"
- "Le 3$^{\text{ème}}$ degré est un premier non avoué"
# Chambert-loir
- "j'ai qu'une envie c'est que le cours soit fini comme ça j'ai pas à faire la preuve"
- "j'ai qu'une envie c'est que le cours soit fini comme ça j'ai pas à faire la preuve"
# Autres
- M. Labroche
- "Si vous voulez parler en cours, c'est simple : Master, Doctorat, Concours de prof, et vous avez le droit de parler en cours !"
- Il ne veut pas lâcher le bord de la piscine, sauf que là c'est pas une piscine, c'est un pédiluve
- à chaque fois que je dis des conneries, c'est du CO2 pour rien
- "je n'oscille pas infiniment entre l'ennui et la souffrance", "c'est parce que tu as ton ordi qui arive à se connecter"
- Evelyne Moreau
- "Ca converge vers $+\infty$"
- "le voisinage de $+\infty$, on y va pas souvent"
- "l'ordre, ça à du sens"
- "c'est ma grand-mère maternelle du côté de mon père"
- "je ne vous fait pas la bise, j'ai les mains mouillées"
- Felix John
- "I'd rather just bring a pillow" ("you don't have to suffer, just bring a pillow !")
- Barbara
- la mort, c'est pas très bon pour la santé
- Max Lemoine
- "je sais écrire mon prénom en anglais"
- "ta tête, elle te va bien !"
- Dario Weinberger
- "Mais non, c'est juste que je suis né avant les autres"
- Catherine :
- c'est un prof : ça s'apprivoise sinon ça mord
- Tours c'est vraiment une boulangerie
- Damien Roverselli
- quand on voit des mains dans les grottes, ont appelle ça de la peinture, donc un coup de poing, ça peut être de l'art
- Maxence Flavier
- Si t'as trop froid c'est que c'est pas assez chaud
- Je veux conduire, mais je louche
- Claudette Louchart
- "Je vais dire un truc, je sait que ça sert à rien, mais je vais le dire quand même"
- E. Escriva et J. Aligon
- Un "sex" de 0.051 ne signifie rien, un IMC de -0.03 n'a aucun sens médical
- Hichem
- "est-ce que j'ai la force de faire l'exercice 3 ?", regarde l'exercice, et 30s plus tard : "bon, on va faire l'exercice 7"
- discussion :
- "t'as compris ?" (Hichem)
- "non." (un étudiant)
- "bah alors viens au tableau."
- L'équation d'une corde vibrante tient compte du fait que les extrémités sont fixes. Pour les guitaristes, je ne sais pas si vous avez remarqué, mais quand la corde pète, le son est nettement moins joli.
- les inégalités, il n'y a rien de plus traître
- C'est dangeureux d'appeller $U$ une réunion
- l'ordre de $x^{k}$ c'est $d$
- parfois il me faut 2 ou 3 jours pour savoir si c'est évident ou pas
- d'aussi loin que je me souvienne, j'ai toujours vécu perso (BanHammer - discord Chez MrPhi)
- Bertrand Gentou (prof d'algorithmique)
- on dépile, on visite, on empile et on dépile les enfants
- je peux l'éliminer, il a pas d'enfants, c'est bon
- c'est pas fait pour être agréable, les machines de Turing
- M. Labroche
- "Si vous voulez parler en cours, c'est simple : Master, Doctorat, Concours de prof, et vous avez le droit de parler en cours !"
- Il ne veut pas lâcher le bord de la piscine, sauf que là c'est pas une piscine, c'est un pédiluve
- à chaque fois que je dis des conneries, c'est du CO2 pour rien
- "je n'oscille pas infiniment entre l'ennui et la souffrance", "c'est parce que tu as ton ordi qui arive à se connecter"
- Evelyne Moreau
- "Ca converge vers $+\infty$"
- "le voisinage de $+\infty$, on y va pas souvent"
- "l'ordre, ça à du sens"
- "c'est ma grand-mère maternelle du côté de mon père"
- "je ne vous fait pas la bise, j'ai les mains mouillées"
- Felix John
- "I'd rather just bring a pillow" ("you don't have to suffer, just bring a pillow !")
- Barbara
- la mort, c'est pas très bon pour la santé
- Max Lemoine
- "je sais écrire mon prénom en anglais"
- "ta tête, elle te va bien !"
- Dario Weinberger
- "Mais non, c'est juste que je suis né avant les autres"
- Catherine :
- c'est un prof : ça s'apprivoise sinon ça mord
- Tours c'est vraiment une boulangerie
- Damien Roverselli
- quand on voit des mains dans les grottes, ont appelle ça de la peinture, donc un coup de poing, ça peut être de l'art
- Maxence Flavier
- Si t'as trop froid c'est que c'est pas assez chaud
- Je veux conduire, mais je louche
- Claudette Louchart
- "Je vais dire un truc, je sait que ça sert à rien, mais je vais le dire quand même"
- E. Escriva et J. Aligon
- Un "sex" de 0.051 ne signifie rien, un IMC de -0.03 n'a aucun sens médical
- Hichem
- "est-ce que j'ai la force de faire l'exercice 3 ?", regarde l'exercice, et 30s plus tard : "bon, on va faire l'exercice 7"
- discussion :
- "t'as compris ?" (Hichem)
- "non." (un étudiant)
- "bah alors viens au tableau."
- L'équation d'une corde vibrante tient compte du fait que les extrémités sont fixes. Pour les guitaristes, je ne sais pas si vous avez remarqué, mais quand la corde pète, le son est nettement moins joli.
- les inégalités, il n'y a rien de plus traître
- C'est dangeureux d'appeller $U$ une réunion
- l'ordre de $x^{k}$ c'est $d$
- parfois il me faut 2 ou 3 jours pour savoir si c'est évident ou pas
- d'aussi loin que je me souvienne, j'ai toujours vécu perso (BanHammer - discord Chez MrPhi)
- Bertrand Gentou (prof d'algorithmique)
- on dépile, on visite, on empile et on dépile les enfants
- je peux l'éliminer, il a pas d'enfants, c'est bon
- c'est pas fait pour être agréable, les machines de Turing
+12
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@@ -0,0 +1,12 @@
---
up:
tags:
aliases:
---
> [!todo] Projets non-commencés
> ```dataview
> LIST title
> FROM ""
> WHERE econtains(up, this.file.link)
> ```
+1 -1
View File
@@ -5,4 +5,4 @@ Un raisonnement est dit _valide_ ssi sa conclusion est la conséquence logique d
# Notation
$$P1, \ldots, Pn \models B$$
Le raisonnement Est valide ssi $B$ est bien [[modèle|modélisé]] par $P1,\ldots,Pn$.
Le raisonnement Est valide ssi $B$ est bien [[théorie des modèles . modèle|modélisé]] par $P1,\ldots,Pn$.
+3 -2
View File
@@ -1,6 +1,7 @@
---
up:: [[relation]]
#s/maths/algèbre
up: "[[relation]]"
tags:
- "#s/maths/algèbre"
---
> [!definition] Relation d'ordre
+1 -1
View File
@@ -1,7 +1,7 @@
#s/maths/logique
----
Une [[proposition]] est _satisfaisable_ si elle admet **au moins un [[modèle]]**.
Une [[proposition]] est _satisfaisable_ si elle admet **au moins un [[théorie des modèles . modèle]]**.
Une [[proposition]] qui n'est pas satisfaisable est une [[contradiction]]
+16
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@@ -0,0 +1,16 @@
---
link: "https://jplattel.nl/project/ov-klok/"
author:
published: 2024-02-14
created: 2026-05-31
description: "Im Joost Plattel, I'd like to call myself an auxiliary technologist. I assist organisations and individuals with technology and help them future strategies."
tags:
- "t/clippings"
---
The [OV Klok](https://ovklok.nl/) is a small hardware project that show the time left before the next departure of public transport you use. Its made with and ESP32 module and 7 segment digit display.
![](https://jplattel.nl/img/ovklok.jpeg)
You can [order one](https://shop.ovklok.nl/) if you live in the Netherlands and use public transport a lot from a specific location. The enclosure is made by pressure-forming plastic in the [Mayku Multiplier](https://mayku.me/multiplier) and a 3D print allowing for different methods of mounting and freestanding use.
The ESP32 runs on Circuit Python and is fully configurable with a USB-C cable through the browser with the use of WebSerial. This skips troublesome setups like captive portals or file editing. Its a simple and calm device allowing you to catch your public transport right on time!
@@ -0,0 +1,173 @@
---
link: https://github.com/dhanushka2001/citeorder
created: 2026-05-11
tags:
- "#t/clippings/github"
- s/informatique
---
[![Logo](https://github.com/user-attachments/assets/43f400c2-ba67-45a9-b196-53757bf9931b#gh-dark-mode-only)](https://github.com/user-attachments/assets/43f400c2-ba67-45a9-b196-53757bf9931b#gh-dark-mode-only)
Simple command-line tool to correctly reorder Footnotes in Markdown files.
> [!tip] Tip
> For those who don't wish to use the command-line, I have made a [Chrome Extension](https://github.com/dhanushka2001/citeorder-github) which adds a toolbar inside GitHub's README.md text editor with a button to reorder footnotes.
## Motivation
Markdown processors that support footnotes (e.g. [GitHubs Markdown engine](https://github.com/github/cmark-gfm), which implements the [GitHub Flavored Markdown](https://github.github.com/gfm) spec) automatically reorder footnotes when converting `.md` files to HTML. However, `citeorder` fixes the ordering in the `.md` file itself, making it neater and easier to manage lots of footnotes. Especially useful when needing to add new footnotes in the middle of a long `.md` file and not having to spend ages reordering every in-text and full-entry footnote manually (🥲).
In-text footnotes (`"Alice here",[^1]`) and full-entry footnotes (`[^1]: Alice`) are a many-to-one relationship. `citeorder` assumes the connections are correct, and relabels them according to the order in which the **in-text footnotes** appear.
## How to use
1. Download the precompiled executable from the latest [release](https://github.com/dhanushka2001/citeorder/releases).
Installation via [Homebrew](https://github.com/dhanushka2001/homebrew-citeorder) (macOS/Ubuntu):
```
brew install dhanushka2001/citeorder/citeorder
```
Installation via the [AUR](https://aur.archlinux.org/packages/citeorder) (Arch):
```
yay -S citeorder
```
Or clone the repo and compile source code
If you want to compile the source code yourself, clone the repo and compile `citeorder.c`:
```
git clone https://github.com/dhanushka2001/citeorder
```
```
gcc -Wall -O2 citeorder.c -o citeorder
```
2. To run, simply enter into the terminal:
```
citeorder input.md
```
where `input.md` is the Markdown file whose Footnotes you want reordered. `citeorder` will keep the original file as is and output the changes to a new file, `input-fixed.md`.
To allow relaxed quote handling, do:
```
citeorder -q input.md
```
For more info and options, run:
```
citeorder -h
```
## Example
`example.md`:
```
"Alice says hi".[^1]
[^1]: Alice
"Bob is here".[^7] "I'm Charlie",[^4] "Daniel!",[^5] here.
[^4]: Charlie
[^3]: Gary
[^5]: Daniel
[^7]: Bob
Is "Ethan"[^8] here?
[^8]: Ethan
"Bob and Charlie here again"[^7][^4]
[^6]: Fred
```
Running:
```
citeorder example.md
```
will produce `example-fixed.md`:
```
"Alice says hi".[^1]
[^1]: Alice
"Bob is here".[^2] "I'm Charlie",[^3] "Daniel!",[^4] here.
[^2]: Bob
[^3]: Charlie
[^4]: Daniel
[^6]: Gary
Is "Ethan"[^5] here?
[^5]: Ethan
"Bob and Charlie here again"[^2][^3]
[^7]: Fred
```
## Cases handled
- No changes needed.
- Stacked in-text footnotes, e.g. `"hello",[^3][^1][^5]``"hello",[^1][^2][^3]`.
- Single punctuation (or none) after end quote, e.g. `"A"[^3] "B",[^2] "C".[^6] "D"![^5]``"A"[^1] "B",[^2] "C".[^3] "D"![^4]`.
- Improper quote, e.g. `"hello[^1]`, `"hello",,[^1]`, `hello"[^1]`, `"hello" [^1]` produces an error message like: `ERROR: in-text citation [^1] not properly quoted (line 5)`. Can ignore this error with the `-q` / `--relaxed-quotes` flag.
- Full-entry footnotes with no matching in-text footnotes simply get bubbled to the end of the ordering.
- In-text footnotes with no matching full-entry footnote produce an error message like: `ERROR: in-text citation [^2] without full-entry (line 3)`.
- Duplicate full-entry footnotes, e.g.
```
[^4]: Alice
[^4]: Bob
```
produces an error message like: `ERROR: duplicate [^4] full-entry citations (line 7 and 8)`.
- Footnotes inside inline code (`"A"[^1]`) and fenced code blocks:
```
"A"[^1]
[^1]: A
[^2]: B
```
are ignored.
- Footnote labels with letters/symbols are supported, and will be relabeled accordingly, e.g. `"A"[^6b]``"A"[^1]`.
- Spaces in the in-text or full-entry footnotes. Spaces outside the label for in-text footnotes, e.g. `"A"[^ Alice ]` are accepted by Markdown processors, and `citeorder` will convert that to `"A"[^1]`. However, for full-entry footnotes, e.g. `[^ 4b ]: Alice`, it is not accepted, and in `citeorder` it will produce an error message like: `ERROR: [^ 4b ] full-entry citation contains a space (line 3)`. For both in-text and full-entry footnotes, spaces **in** the label itself, e.g. `"A"[^4 b]`, `[^4 b]: Alice`, are not accepted, and in `citeorder` you will get an error message.
- In-text or full-entry footnote missing a label, e.g. `"A"[^]`, will produce an error message like: `ERROR: in-text citation [^] missing label (line 7)`.
- Multiline quote:
```
"T"[^4]
"This quote takes
up multiple lines
but is still valid",[^3]
"H",[^6]
[^4]: T
[^6]: H
[^3]: Multiline quote
```
becomes:
```
"T"[^1]
"This quote takes
up multiple lines
but is still valid",[^2]
"H",[^3]
[^1]: T
[^2]: Multiline quote
[^3]: H
```
- Duplicate full-entry footnotes, e.g.
```
"A"[^dupe], "B"[^dupe]
[^dupe]: A
[^dupe]: B
"C"[^dupe]
[^dupe]: C
"D"[^1]
[^1]: D
```
can be auto-incremented using the `-d` / `--relaxed-duplicates` flag (must be only ONE duplicate footnote label, and must have an equal number of full-entry and in-text duplicates):
```
"A"[^1], "B"[^2]
[^1]: A
[^2]: B
"C"[^3]
[^3]: C
"D"[^4]
[^4]: D
```
@@ -0,0 +1,161 @@
---
link: "https://github.com/sosedoff/lunchy-go"
created: 2026-06-05
tags:
- "#t/clippings/github"
---
## lunchy-go
A friendly wrapper for launchctl. Start your agents and go to lunch!
This is a port of original [lunchy](https://github.com/mperham/lunchy) ruby gem by Mike Perham with extra functionality.
## Overview
Don't you hate OSX's launchctl? You have to give it exact filenames. The syntax is annoying different from Linux's nice, simple init system and overly verbose. It's just not a very developer-friendly tool.
Lunchy aims to be that friendly tool by wrapping launchctl and providing a few simple operations that you perform all the time:
- ls \[pattern\]
- start \[pattern\]
- stop \[pattern\]
- restart \[pattern\]
- status, ps \[pattern\]
- install \[file\]
- show \[pattern\]
- edit \[pattern\]
- remove, rm \[pattern\]
- scan \[path\]
where pattern is just a substring that matches the agent's plist filename.
So instead of:
```
$ launchctl load ~/Library/LaunchAgents/io.redis.redis-server.plist
```
you can do this:
```
$ lunchy start redis
```
and:
```
$ lunchy ls
com.danga.memcached
com.google.keystone.agent
com.mysql.mysqld
io.redis.redis-server
org.mongodb.mongod
```
## Install
You can install binary by running the following bash command:
```
curl -s https://raw.githubusercontent.com/sosedoff/lunchy-go/master/install.sh | bash
```
#### Homebrew
Install using [Homebrew](https://brew.sh/):
```
brew install lunchy-go
```
#### Binary Releases
Precompiled binaries are available on Github: [https://github.com/sosedoff/lunchy-go/releases](https://github.com/sosedoff/lunchy-go/releases)
#### Build from source
Build source code with Go 1.2+:
```
git clone https://github.com/sosedoff/lunchy-go.git $GOPATH/src/lunchy
cd lunchy
go build
mv ./lunchy-go /usr/local/bin/lunchy
```
## Usage
Add a new plist:
```
# Install plist
$ lunchy install /usr/local/Cellar/redis/2.8.1/homebrew.mxcl.redis.plist
```
Manage services:
```
$ lunchy start redis
$ lunchy stop redis
$ lunchy restart redis
$ lunchy status redis
```
If you have multiple plists from homebrew, you can simple control all of them:
```
$ lunchy status
homebrew.mxcl.elasticsearch
homebrew.mxcl.mysql
homebrew.mxcl.postgresql
homebrew.mxcl.redis
# Will stop all processes prefixed by "homebrew"
$ lunchy stop homebrew
```
Manage plists:
```
$ lunchy show redis
$ lunchy edit redis
```
Scan directory for existing plists:
```
$ lunchy scan /usr/local/Cellar
```
Scan all homebrew plists:
```
$ lunchy scan homebrew
```
## Profiles
When switching between different projects you might find yourself stopping and starting lots of different daemons in order to reduce memory usage. This is all good but there's a better way of doing it. Enter lunchy profiles.
Profile file `.lunchy` should be placed under your project's root directory and include a list of services that needs to be started or stopped. Example:
```
postgres
redis
elasticsearch
```
Then you can simply run the following command to start/stop/restart ALL of them at once:
```
lunchy start
lunchy stop
lunchy restart
```
## License
The MIT License (MIT)
Copyright (c) 2013-2015 Dan Sosedoff, [dan.sosedoff@gmail.com](mailto:dan.sosedoff@gmail.com)
+29
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@@ -0,0 +1,29 @@
---
genre:
- "[[Drame]]"
- "[[Romantique]]"
- "[[Thriller]]"
director:
- "[[Park Chan-wook]]"
rating:
scoreImdb: 8.1
cast:
- "[[Kim Min-hee]]"
- "[[Ha Jung-woo]]"
- "[[Cho Jin-woong]]"
cover: "https://m.media-amazon.com/images/M/MV5BMTE5MDAyZjMtYjNhMi00YTE3LThhNjgtNTNiNWZhNzVkNjFkXkEyXkFqcGc@._V1_.jpg"
plot: "Une femme est embauchée en tant que servante d'une héritière japonaise, mais elle est secrètement impliquée dans un complot visant à l'escroquer."
year: 2016
created: 2026-05-25
tags:
- "t/source/film"
- "s/art/cinema"
nb_times_seen: "0"
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
+29
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@@ -0,0 +1,29 @@
---
genre:
- "[[Drame]]"
- "[[Fantastique]]"
- "[[Horreur]]"
director:
- "[[Park Chan-wook]]"
rating:
scoreImdb: 7.1
cast:
- "[[Song Kang-ho]]"
- "[[Kim Ok-bin]]"
- "[[Choi Hee-jin]]"
cover: "https://m.media-amazon.com/images/M/MV5BMDIxMTk2MjAtYTgzNy00NDE5LTg2MWQtYjM5ODBhODZkN2M4XkEyXkFqcGc@._V1_.jpg"
plot: "A la suite d'une expérience médicale ratée, un prêtre devient un vampire. Sa vie ascétique change du tout au tout."
year: 2009
created: 2026-05-25
tags:
- "t/source/film"
- "s/art/cinema"
nb_times_seen: "0"
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
@@ -0,0 +1,22 @@
---
genre:
director:
rating:
scoreImdb:
cast:
cover:
plot: Trailer for the classic comedy Some Like It Hot, starring Tony Curtis, Jack Lemmon, and Marilyn Monroe
year: 1959
created: 2026-05-25
tags:
- t/source/film
- s/art/cinema
nb_times_seen: "0"
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
+29
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@@ -0,0 +1,29 @@
---
genre:
- "[[Drame]]"
- "[[Horreur]]"
- "[[Science-fiction]]"
director:
- "[[Bong Joon Ho]]"
rating:
scoreImdb: 7.1
cast:
- "[[Song Kang-ho]]"
- "[[Byun Hee-Bong]]"
- "[[Park Hae-il]]"
cover: "https://m.media-amazon.com/images/M/MV5BOGY1ZDcyNTQtOTdkMy00NzY0LThiM2ItNzM4ZmNhZmQzOGU0XkEyXkFqcGc@._V1_.jpg"
plot: "Un monstre émerge du fleuve Han à Séoul et se met à attaquer la foule. La famille aimante d'une victime fait tout son possible pour la sauver des griffes de la créature."
year: 2006
created: 2026-05-25
tags:
- "t/source/film"
- "s/art/cinema"
nb_times_seen: "0"
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
+30
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@@ -0,0 +1,30 @@
---
genre:
- "[[Animation]]"
- "[[Aventure]]"
- "[[Comédie]]"
director:
- "[[Nicolas Athane]]"
- "[[Marco Nguyen]]"
rating:
scoreImdb: 6.8
cast:
- "[[François Sagat]]"
- "[[Jérémy Gillet]]"
- "[[Philippe Katerine]]"
cover: https://m.media-amazon.com/images/M/MV5BOWY2MTE5NDUtOGExNC00MTQwLTg3NTAtZmQ3ZDUwZjYwYzkzXkEyXkFqcGc@._V1_.jpg
plot: Jim, icône sexy de la scène gay parisienne, voit sa vie basculer lorsqu'il contracte l'Hétérose, un étrange virus qui transforme les hommes gays en hétérosexuels .
year: 2026
created: 2026-05-25
tags:
- t/source/film
- s/art/cinema
nb_times_seen: 0
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
+29
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@@ -0,0 +1,29 @@
---
genre:
- "[[Drame]]"
- "[[Fantastique]]"
- "[[Mystère]]"
director:
- "[[Richard Schenkman]]"
rating:
scoreImdb: 7.8
cast:
- "[[David Lee Smith]]"
- "[[Tony Todd]]"
- "[[John Billingsley]]"
cover: "https://m.media-amazon.com/images/M/MV5BOTE1NGYxNjgtYmVlMS00ODEwLTg2NjAtMTdjODMzY2I1ZjZmXkEyXkFqcGc@._V1_.jpg"
plot: "Une fête d'au revoir impromptue pour le Professeur John Oldman se transforme en interrogatoire mystérieux après que l'universitaire sur le départ révèle à ses collègues un passé plus étrange qu'ils n'auraient pu s'imaginer."
year: 2007
created: 2026-05-26
tags:
- "t/source/film"
- "s/art/cinema"
nb_times_seen: "0"
date_last_seen:
---
`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
- score`VIEW[IMDB : {scoreImdb}/10][text]`
- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`
+187
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@@ -0,0 +1,187 @@
---
up:
- "[[ensemble]]"
tags:
- s/maths/logique
aliases:
---
Cette théorie ne se base pas sur des ensembles directement, mais sur des **classes**.
Les classes sont caractérisées par $\in$, autrement dit une classe est définie par le prédicat indiquant ce qu'elle contient.
# Définitions et Axiomes
> [!definition] Classe
> Une classe $C$ est un objet caractérisé par sa relation d'appartenance, c'est-à-dire que pour tout objet $x$ on pourra dire si $x \in C$ ou non.
^def-classe
> [!proposition]+ Axiome d'extentionnalité
> Deux choses contenant les mêmes éléments sont égales.
> Autrement dit, $C_1 = C_2$ si et seulement si $\forall x,\quad x \in C_1 \iff x \in C_2$
^ax-extentionnalite
> [!definition] Inclusion
> La relation d'inclusion, notée $\subseteq$ est définie par :
> $C_1 \subseteq C_2 \iff \text{pour toute classe } X \text{ avec } X \in C_1 \text{ on a } X\in C_2$
^def-inclusion
> [!definition] Ensemble
> Une classe $A$ est un **ensemble** s'il existe une classe $C$ telle que $A \in C$.
> - i l'axiome d'extentionnalité s'applique également sur les ensembles
> - i on note $\mathcal{M}$ le prédicat "est un ensemble" ($\mathcal{M}(x) \iff x \text{ est un ensemble}$)
^def-ensemble
> [!definition] Union et Intersection
> Soient $C_1$ et $C_2$ deux classes
> - $C_1 \cup C_2$ est une classe dont les éléments sont les $X$ qui appartiennent à $C_1$ ou à $C_2$
> - $C_1 \cap C_2$ est une classe dont les éléments sont les $X$ qui appartiennent à $C_1$ et à $C_2$
> - i on sait par l'axiome d'extentionnalité que $C_1 \cup C_2$ et $C_1 \cap C_2$ sont uniquement déterminés par ces définitions
^def-union-intersection
> [!definition] Complémentaire
> Soit $C$ une classe
> $C^{\complement}$ est la classe qui a pour éléments les $X$ tels que $X \notin C$
> - i on sait par l'axiome d'extentionnalité que $C^{\complement}$ est uniquement déterminé par ces définitions
>
^def-complementaire
> [!proposition]+ Axiome d'intersection
> Si $x$ est un ensemble, si $C$ est une classe, alors $x \cap C$ est un ensemble
> - i Par conséquence, si une classe $C$ est contenue dans un ensemble $A$, alors $C$ est un ensemble aussi.
> - dem car $C \subseteq A$ entraine $C = C \cap A$
^ax-intersection
> [!proposition]+ Axiome de la paire
> Si $x$ et $y$ sont des ensemble, alors il existe un ensemble dont les seuls éléments sont $x$ et $y$.
> $\tiny\mathcal{M}(x) \wedge \mathcal{M}(y) \implies (\exists z,\quad \mathcal{M}(z) \wedge x \in z \wedge y \in z \wedge (\forall t,\quad t \in z \implies (t=x \vee t=z)))$
> - i par l'axiome d'extentionnalité, on sait qu'il n'existe qu'un seul tel ensemble, que l'on note $\{ x, y \}$
> - i si $x = y$ on note simplement $\{ x \}$, c'est un **singleton**
>
> > [!proposition]+ Construction des couples (Kuratowski)
> > Si $x$ et $y$ sont des ensembles, on pose :
> > $(x, y) = \{ \{ x \}, \{ x, y \} \}$
^ax-paire
> [!proposition]+ égalité sur les couples
> Soient $x, y, x', y'$ des ensembles
> $(x, y) = (x', y') \iff x=x' \wedge y=y'$
> > [!démonstration]- Démonstration
> > - $\boxed{\implies}$ Supposons que $x=x'$ et $y=y'$, on a alors $\{ x, y \} = \{ x', y' \}$ et $\{ x \} = \{ x' \}$ par l'axiome d'extension.
> > Alors, à nouveau par extentionnalité, on a $\{ \{ x \}, \{ x, y \} \} = \{ \{ x' \}, \{ x', y' \} \}$
> > - $\boxed{\impliedby}$ Supposons réciproquement que $(x, y) = (x', y')$
> > On a alors : $\{ \{ x \}, \{ x, y \} \} = \{ \{ x' \}, \{ x', y' \} \}$
> > Il suit par extension que l'un des cas suivants est réalisé :
> > - soit $\{ x \} = \{ x' \}$ et $\{ x, y \} = \{ x', y' \}$
> > dans ce cas, on a $x=x'$ par extension, et de là il est évident aussi que $y = y'$
> > - soit $\{ x \} = \{ x', y' \}$ et $\{ x, y \} = \{ x' \}$
> > dans ce cas on sait que l'on doit avoir $x=y$ et $x'=y'$, et on en déduit $\{ x \} = x'$ et $y=y'$
> > Les autres cas peuvent être éliminés par extentionnalité.
> [!proposition]+ n-uplets
> On peut construire les triplets, quadruplets etc. à partir des couples :
> - $(x, y, z) = ((x, y), z)$
> - $(x, y, z, w) = (((x, y), z), w)$
> - $\vdots$
> [!proposition]+ Axiome : graphe de la relation $\in$
> Il existe une classe $E$ telle que pour tous les ensemble $x, y$ on a $(x, y) \in E$ si et seulement si $x \in y$.
> $\boxed{(x, y) \in E \iff x \in y}$
> $E$ est le **graphe** de la relation $\in$
> [!proposition]+ Axiome : existence du domaine
> Si $C$ est une classe, il existe une classe notée $\operatorname{dom}(C)$ telle que pour tout ensemble $x$ on aie $x \in \operatorname{dom}(C)$ si et seulement s'il existe un ensemble $y$ tel que $(x, y) \in C$.
> $\boxed{x \in \operatorname{dom}(C) \iff \exists y \text{ ensemble},\quad (x, y) \in C}$
> - i On dit que $\operatorname{dom}(C)$ est le **domaine** de $C$
^ax-domaine
> [!proposition]+ Axiome : existence du codomaine
> Si $C$ est une classe, il existe une classe notée $\operatorname{codom}(C)$ telle que pour tout ensemble $y$ on aie $y \in \operatorname{codom}(C)$ si et seulement s'il existe un ensemble $x$ tel que $(x, y) \in C$.
> $\boxed{y \in \operatorname{codom}(C) \iff \exists x \text{ ensemble},\quad (x, y) \in C}$
> - i On dit que $\operatorname{codom}(C)$ est le **codomaine** de $C$
^ax-codomaine
> [!proposition]+ Axiome : existence d'une classe de domaine $C$
> Si $C$ est une classe, il existe une classe $C'$ dont $C$ est le domaine ($\operatorname{dom}(C') = C$), autrement dit :
> il existe une classe $C'$ telle que $\forall y \text{ ensemble},\quad (x, y) \in C' \iff x \in C$
^ax-de-domaine
> [!proposition]+ Axiome : existence d'une classe de codomaine $C$
> Si $C$ est une classe, il existe une classe $C'$ dont $C$ est le codomaine ($\operatorname{codom}(C') = C$), autrement dit :
> il existe une classe $C'$ telle que $\forall x \text{ ensemble},\quad (x, y) \in C'$
^ax-de-codomaine
> [!proposition]+ Axiome : permutation des triplets
> Soit $C$ une classe, alors :
> - il existe une classe $D$ telle que pour tous les ensembles $x, y, z$ on aie $(x, y, z) \in D \iff (y, x, z) \in C$
> - il existe une classe $D'$ telle que pour tout les ensemble $x, y, z$ on aie $(x, y, z) \in D' \iff (x, z, y) \in C$
> - i ces classes ne sont pas uniquement déterminées par l'axiome d'extension, car leurs "définitions" prescrivent uniquement leurs couples ou trouples.
> [!definition]+ Classe vide
> Il existe une et une seule classe qui n'a aucun élément.
> On dit que c'est la classe vide et on la note $\emptyset$
> > [!démonstration]- Démonstration (existence et unicité)
> > L'axiome sue le graphe de la relation $\in$ fournit une classe $E$.
> > On peut alors former la classe $E \cap E^{\complement}$ qui, par construction, n'a aucun élément.
> > D'après l'axiome d'extentionnalité, c'est la seule telle classe.
> [!proposition]+ Axiome (NBG) : ensemble vide
> $\emptyset$ est un ensemble
> - i Sans cet axiome, rien ne garantit l'existence d'ensembles
> [!definition] Univers
> La classe $U = \emptyset^{\complement}$ est appelée **univers**
> Par définition on a $x \in U$ pour tout ensemble $x$.
> Pour toute classe $C$ on a $C \subseteq U$
> - i Le [[paradoxe de Russell]] montre qu'il existe une classe $R$ qui n'est pas un ensemble. Comme toute sous-classe d'un ensemble est un ensemble aussi, on sait alors que $U$ n'est pas un ensemble.
^definition
> [!definition] Union d'une classe
> Soit $C$ une classe
> Il existe une unique classe dont les éléments sont les éléments des éléments de $C$.
> On note cette classe $\cup C$ (l'union de $C$).
> > [!démonstration]- Démonstration (existence et unicité)
> > L'existence est évidente par définition, mais on peut également utiliser l'union de éléments de $C$.
> > L'unicité est donnée par l'axiome d'extentionnalité.
^def-union-monadique
> [!proposition]+ Produit cartésien
> Soient $A$ et $B$ des classes, il existe une unique classe dont les éléemnts sont les $(x, y)$ avec $x \in A$ et $y \in B$.
> On note cette classe $A \times B$
> ---
> Plus généralement, soit $n \in \mathbb{N}^{*}$, soient $A_1, \dots, A_{n}$ des classes
> Il existe une classe et une seule dont les éléments sont les $n$-uplets $(x_1, \dots, x_{n})$ avec $x_1 \in A_1, \dots, x_{n} \in A_{n}$
> On note cette classe $A_1 \times \cdots \times A_{n}$
> - i Lorsque $A_1 = \cdots = A_{n}$ on note $A_1 \times \cdots \times A_{n} = A^{n}$
>
> > [!démonstration]- Démonstration (existence et unicité)
> > On sait par l'axiome d'extensionnalité qu'il existe au plus une telle classe (unicité).
> > Il existe une classe $A'$ telle que $\forall x,\quad (x, y) \in A' \iff y \in A$ (telle que $A = \operatorname{dom}(A')$)
> > Il existe une classe $B'$ telle que $\forall y,\quad (x, y) \in B' \iff x \in B$ (telle que $B = \operatorname{codom}(B')$)
> > Alors, $A' \cap B'$ existe (par axiome d'intersection) et convient :
> > $\forall x,\forall y,\quad (x, y) \in A'\cap B' \implies \begin{cases} x \in A \text{ car } (x, y) \in A' \cap B' \implies (x, y) \in A' \implies x \in A\\ y \in B \text{ car } (x, y) \in B' \end{cases}$
> >
> [!proposition]+ Axiome (NBG) : Union d'un ensemble
> Si $x$ est un ensemble, alors $\cup x$ est un ensemble aussi.
> $\mathcal{M}(x) \implies \mathcal{M}(\cup x)$
## Graphes
> [!definition] Graphe
> Une classe $C$ est un **graphe** si tous ses éléments sont des couples.
> [!proposition]+ Image directe
> Soit $G$ un graphe et $C$ une classe.
> Il existe une unique classe (notée $G[C]$ ou $G\langle C \rangle$) dont les éléments sont les ensembles $y$ tels qu'il existe $x \in C$ vérifiant $(x, y) \in G$
> Autrement dit :
> $G[C] = \text{les ensembles } y \text{ tels que } \exists x,\quad x \in C \wedge (x, y) \in G$
> ou encore : $y \in G[C] \iff \mathcal{M}(y) \wedge (\exists x,\quad x \in C \wedge (x, y) \in G)$
> > [!démonstration]- Démonstration (existence et unicité)
> > La classe $G \cap (C \times U)$ a pour éléments les couples $(x, y)$ tels que $x \in C$ et $(x, y) \in G$.
> > Son [[théorie des ensemble NBC#^ax-codomaine|codomaine]] convient : $G[C] = \operatorname{codom}(G \cap (C \times U))$
> > Cela montre l'existence de $G[C]$
> > Son unicité est donnée par extentionnalité
> [!definition] Classe fonctionnelle
> Une classe $F$ est dite **fonctionnelle** si pour tous ensembles $x, y, z$ tels que $(x, y) \in F$ et $(x, z) \in F$ on a $y = z$
@@ -0,0 +1,11 @@
---
up:
tags:
aliases:
---
> [!definition] [[théorie des modèles . modèle]]
> Soit une [[théorie des modèles.théorie|théorie]] $T$ et une [[formule logique close]] $F$ du langage $L$
> $F$ est **conséquence sémantique** de $T$ (ou simplement conséquence de $T$) si et seulement si toute [[théorie des modèles . 𝐿-structure|𝐿-structure]] qui est modèle de $T$ est aussi modèle de $F$.
>
^definition
@@ -0,0 +1,20 @@
---
up:
- "[[théorie des modèles . formule universellement valide|formule universellement valide]]"
tags:
- s/maths/logique/modèles
aliases:
- formule contradictoire
- contradictoire
- formule inconsistante
- inconsistante
---
> [!definition] [[théorie des modèles . formule contradictoire]]
> Une [[formule logique close|formule close]] d'un [[langage des prédicats du premier ordre|langage]] $L$ est **contradictoire** (ou **inconsistante**) si et seulement sa négation est [[théorie des modèles . formule universellement valide|universellement valide]]
^definition
# Propriétés
# Exemples
@@ -0,0 +1,22 @@
---
up:
- "[[théorie des modèles]]"
tags:
- s/maths/logique/modèles
aliases:
- formule universellement valide
- universellement valide
---
> [!definition] [[théorie des modèles . formule universellement valide]]
> Soit $L$ un [[langage des prédicats du premier ordre|langage du premier ordre]]
> Une [[formule logique close|formule close]] de $L$ est **universellement valide** si et seulement si elle est satisfaite dans toute $L$-structure. (On dit parfois simplement « formule valide »).
> On note $\vdash^{*}F$ pour « $F$ est universellement valide »
^definition
# Propriétés
# Exemples
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---
up:
- "[[théorie des modèles]]"
tags:
- "#s/maths/logique/modèles"
---
# Propriétés
# Exemples
---
Un modèle logique est **une [[interprétation]] particulière d'une [[proposition]]**.
On dit qu'une interprétation $I$ est un [[théorie des modèles . modèle]] d'une [[proposition]] logique $\Phi$ ssi $I(\Phi) = \mathbb{V}$.
Si toutes les interprétations de $P$ sont aussi des modèles de $P$, alors on dit que $P$ est une [[tautologie]].
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---
up:
- "[[logique]]"
tags:
- s/maths/logique/modèles
aliases:
---
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
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---
up:
tags:
aliases:
---
```breadcrumbs
title: "Sous-notes"
type: tree
collapse: true
show-attributes: [field]
field-groups: [downs]
depth: [0, 0]
```
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@@ -8,6 +8,8 @@ aliases:
- réalisme
share_link: https://share.note.sx/1ckfabvc#5mTtkYDXoj/rv3sTmsdUqSMHMJStpRbFWBojhX6cpTY
share_updated: 2025-09-15T13:06:31+02:00
sibling:
- "[[épistémologie . antiréalisme|antiréalisme]]"
---
Idée qu'une théorie scientifique est la rencontre de son objet.