device-52.home 2026-3-21:19:6:3
This commit is contained in:
oskar
3
.obsidian/community-plugins.json
vendored
3
.obsidian/community-plugins.json
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@@ -42,5 +42,6 @@
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"obsidian-kanban",
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"obsidian-pandoc",
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"obsidian-enhancing-export",
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"heatmap-tracker"
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"contribution-graph",
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"header-enhancer"
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]
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@@ -3,6 +3,10 @@
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{
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||||
"folderPath": "/",
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"templateName": "default new note"
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},
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{
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"folderPath": "daily",
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"templateName": "daily note"
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}
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],
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"disablePrompt": false,
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4
.obsidian/plugins/breadcrumbs/data.json
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4
.obsidian/plugins/breadcrumbs/data.json
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@@ -631,7 +631,7 @@
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"prevs"
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],
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"lock_view": false,
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"lock_path": "daily/2026-03-21.md"
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"lock_path": "suites finies d'entiers comme fonctions récursives primitives.md"
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},
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"tree": {
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"collapse": false,
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@@ -651,7 +651,7 @@
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"alias": false
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},
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"lock_view": false,
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"lock_path": ""
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"lock_path": "suites finies d'entiers comme fonctions récursives primitives.md"
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}
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},
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"codeblocks": {
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26
.obsidian/plugins/header-enhancer/data.json
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Normal file
26
.obsidian/plugins/header-enhancer/data.json
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Normal file
@@ -0,0 +1,26 @@
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{
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"language": "en",
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"showOnStatusBar": true,
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"showOnSidebar": true,
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"isAutoDetectHeaderLevel": false,
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"startHeaderLevel": 1,
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"endHeaderLevel": 6,
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"autoNumberingMode": "on",
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"autoNumberingStartNumber": "1",
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"autoNumberingSeparator": ".",
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"autoNumberingHeaderSeparator": "\t",
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"updateBacklinks": false,
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"yamlFallbackMode": "use_default",
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"yamlDefaultStartLevel": 2,
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"yamlDefaultEndLevel": 6,
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"yamlDefaultStartNumber": "1",
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"yamlDefaultSeparator": ".",
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"globalAutoNumberingEnabled": true,
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"perDocumentStates": "{\"suite finies d'entiers.md\":false}",
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"isSeparateHeaderFont": false,
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"headerFontFamily": "inherit",
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"headerFontSize": "inherit",
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"isSeparateTitleFont": false,
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"titleFontFamily": "inherit",
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"titleFontSize": "inherit"
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}
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3524
.obsidian/plugins/header-enhancer/main.js
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Normal file
3524
.obsidian/plugins/header-enhancer/main.js
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Normal file
File diff suppressed because it is too large
Load Diff
11
.obsidian/plugins/header-enhancer/manifest.json
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Normal file
11
.obsidian/plugins/header-enhancer/manifest.json
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Normal file
@@ -0,0 +1,11 @@
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{
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"id": "header-enhancer",
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"name": "Header Enhancer",
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"version": "0.5.1",
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"minAppVersion": "0.14.0",
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"description": "Level up your headers, customize your notes. Header Enhancer makes your notes header better and more useful.",
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"author": "Hobee Liu",
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"authorUrl": "https://github.com/HoBeedzc",
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"fundingUrl": "https://bmc.link/hobee",
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"isDesktopOnly": false
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}
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8
.obsidian/plugins/header-enhancer/styles.css
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8
.obsidian/plugins/header-enhancer/styles.css
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@@ -0,0 +1,8 @@
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/*
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This CSS file will be included with your plugin, and
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available in the app when your plugin is enabled.
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If your plugin does not need CSS, delete this file.
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*/
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123
.obsidian/plugins/heatmap-tracker/main.js
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123
.obsidian/plugins/heatmap-tracker/main.js
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File diff suppressed because one or more lines are too long
12
.obsidian/plugins/heatmap-tracker/manifest.json
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12
.obsidian/plugins/heatmap-tracker/manifest.json
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@@ -1,12 +0,0 @@
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{
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"id": "heatmap-tracker",
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"name": "Heatmap Tracker",
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"version": "2.1.7",
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"minAppVersion": "0.1.0",
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"description": "Visualize your activity and track goals, progress, habits, tasks, exercise, finances, and more—all in a single, interactive heatmap!",
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"author": "Maksim Rubanau",
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"isDesktopOnly": false,
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"fundingUrl": {
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"Buy Me a Coffee": "https://www.buymeacoffee.com/mrubanau"
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}
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}
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1
.obsidian/plugins/heatmap-tracker/styles.css
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1
.obsidian/plugins/heatmap-tracker/styles.css
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@@ -113,7 +113,7 @@
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"library2": {
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"type": "excalidrawlib",
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"version": 2,
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"source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.20.2",
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"source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.21.2",
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"libraryItems": []
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},
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"imageElementNotice": true,
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||||
@@ -5,7 +5,7 @@
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{
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"id": 1,
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"name": "Ma bibliothèque",
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"lastUpdate": 1774111558215
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"lastUpdate": 1774114564025
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}
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],
|
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"renderCitations": true,
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3
.obsidian/types.json
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3
.obsidian/types.json
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@@ -95,6 +95,7 @@
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"lt-disabledCategories": "multitext",
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"excalidraw-export-internal-links": "checkbox",
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"date-rendu": "date",
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"TQ_show_toolbar": "checkbox"
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"TQ_show_toolbar": "checkbox",
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"sport": "checkbox"
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}
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}
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@@ -9,4 +9,10 @@ date-rendu:
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- 2026-03-26
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type-rendu:
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- partiel
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BC-list-note-field: down
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---
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- [[fonction récursive primitive]]
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- [[schéma mu borné|schéma µ borné]]
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- [[suites finies d'entiers comme fonctions récursives primitives]]
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- [[ensemble récursif primitif]]
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||||
@@ -12,7 +12,7 @@ type: tree
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collapse: false
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show-attributes: [field]
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field-groups: [downs]
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depth: [0, 0]
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depth: [0, 1]
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```
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||||
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||||
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@@ -0,0 +1,186 @@
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---
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||||
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excalidraw-plugin: parsed
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tags: [excalidraw]
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||||
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||||
---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
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||||
# Excalidraw Data
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||||
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||||
## Text Elements
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||||
(0, 0) ^JA63goKG
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|
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(0, 0) ^6tqLjjL9
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|
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(0, 0) ^qDjoBHEx
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(0, 0) ^lGM9MteR
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(0, 0) ^FyOPD2fS
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(0, 0) ^2pI7yato
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(0, 0) ^h3UuIkDh
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(0, 0) ^8851sTNL
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(0, 0) ^Qspw30zN
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(0, 0) ^8A7op9wf
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1 ^18ZljkeX
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2 ^3QOLh4aV
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0 ^jiLeEZkr
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3 ^zVEbLbb6
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4 ^J4pGIH91
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5 ^4TRNOjkQ
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|
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6 ^FMMDc4pu
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7 ^GZaf2kRj
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8 ^JYbC6kRA
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9 ^Ca9c8U1W
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||||
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||||
%%
|
||||
## Drawing
|
||||
```compressed-json
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|
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||||
|
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|
||||
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||||
2mT607aZhrsqPpSN2NZR+Moq3H4J/+wHfaEZn7howO87rrAfJXiVT5vAy+fD1vmPMQC7UQ7Jc9XA3Plq25J57HAgofP811C1Uu/UYWlTWFlU2qZO5nc7Tph01SHt8OGn/DlF67XYdNOKnPdypi0+gBj5x8E+SfJb7qfm1OnppsGgI1RaCNu7vTZe4gA9/086G4jKnrXkonFxwA4APIJ2ChugCtQMg5QM8KQBsgbAGAhABABQD9DYKqyrIeHwj76D
|
||||
|
||||
kCRAmCK0I0H0A8gq1gXzBpNxR+7T0fMPw/Uy6FnXLkfasfH+kBwiOD2xSP7AHj8rno/Mfyj+nbj/J8M/0gTP/WtF7v20/6fUANH+kCaDM7wfdPtn/z/R+SJ9b/PMn6j/R84RpWidkX3z4F/6B5fFoyJkr7F8q+LIK7goDL4p8Y/7vDFlTPr/Z/6AtwER5i1EZN+i/Zf6QR1dp7qLMAzIpAN3qb/F+U+YYQvxUCb+YDYAYQnIAKBVjXixtJgxkGNQ
|
||||
|
||||
ee+t7R/fyIfAPuQ6iThooq+OHVBYXV6+jAbAAwJtoYAEANIS6bg+8MKLu+VfQv9kRIGQRI+SQJAeB+D6r/EAeQCAUuDaJoUkBqgfUi37gE0DBBehLf2R0vD9DIgy6ygAkH+EkFwQx/vAA4KMmihpXlIygTMIyHKCkBh/uAUf3R3H/r/eAm/l6aBCL+2/1onPhAJL6YicBIbZk5oKtKYC0Wl4mQTv939VeQ0iATfuTyUAbhA/GP3WBSJNgf8zzGQ8
|
||||
|
||||
IUgF6BKoP/gEp/+TAB35d+JiD3BF+dgCGCFG2QFyANwcAG34aI4Aff76i4uNgBMQjAOBCZ+xRp7otG/IGkCYBtiB0hCAUIAYCO+6EI16TuIjAYCJGwQMQGq4zXvgChA/hMQHYBuAceRF+jgMwB3+kCFkBQQ1QJkBUE6AYNKx6QiIECsgTAJkDOIB8nwGGcudEkqoBkAWDa50IZiSoIBuAN94NSyga45jY4AAvBn64QE1J2wDkEAA
|
||||
```
|
||||
%%
|
||||
File diff suppressed because one or more lines are too long
|
After Width: | Height: | Size: 19 KiB |
23
daily/2026-03-20.md
Normal file
23
daily/2026-03-20.md
Normal file
@@ -0,0 +1,23 @@
|
||||
---
|
||||
sport: true
|
||||
---
|
||||
|
||||
# Todo
|
||||
|
||||
```tasks
|
||||
due 2026-03-20
|
||||
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 2026-03-20
|
||||
short mode
|
||||
```
|
||||
# I am gratefull to
|
||||
|
||||
@@ -1,3 +1,7 @@
|
||||
---
|
||||
sport: "true"
|
||||
---
|
||||
|
||||
# Todo
|
||||
|
||||
```tasks
|
||||
@@ -5,6 +9,7 @@ due 2026-03-21
|
||||
not done
|
||||
```
|
||||
# I did
|
||||
- [ ] #task test
|
||||
|
||||
> [!smallquery]- Modified files
|
||||
> ```dataview
|
||||
@@ -17,3 +22,5 @@ short mode
|
||||
```
|
||||
# I am gratefull to
|
||||
|
||||
|
||||
|
||||
|
||||
23
daily/2026-03-22.md
Normal file
23
daily/2026-03-22.md
Normal file
@@ -0,0 +1,23 @@
|
||||
---
|
||||
sport: true
|
||||
---
|
||||
|
||||
# Todo
|
||||
|
||||
```tasks
|
||||
due 2026-03-22
|
||||
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 2026-03-22
|
||||
short mode
|
||||
```
|
||||
# I am gratefull to
|
||||
|
||||
@@ -6,7 +6,7 @@ salaire (net mensuel) **médian** en france :: 1 850€/mois
|
||||
<!--SR:!2024-10-18,284,250-->
|
||||
|
||||
salaire (net mensuel) **médian** en france **pour un couple** :: 3 857€/mois
|
||||
<!--SR:!2024-09-04,16,150-->
|
||||
<!--SR:!2026-03-21,1,130-->
|
||||
|
||||
pourcentage de fils/filles d'ouvriers qui **sortent** de l'université dans des filières d'excellence :: 3%
|
||||
<!--SR:!2027-08-31,1107,310-->
|
||||
|
||||
@@ -22,18 +22,3 @@ aliases:
|
||||
> > $\pi(n+1) = \mu p \leq (n+1)! \quad \left(\mathrm{sg}(p \dot{-}\pi( n)) \cdot \left( 1\dot{-} \mathrm{sg} \left( \sum\limits_{d=1}^{d=p}d|p \right) \right) \right)$
|
||||
^recursive-primitive
|
||||
# Exemples
|
||||
|
||||
```heatmap-tracker
|
||||
heatmapTitle: Test
|
||||
heatmapSubtitle: ""
|
||||
property: nb_times_seen
|
||||
year: 2025
|
||||
separateMonths: true
|
||||
showCurrentDayBorder: true
|
||||
disableFileCreation: false
|
||||
excludeFalsy: false
|
||||
colorScheme:
|
||||
paletteName: default
|
||||
ui: {}
|
||||
```
|
||||
|
||||
|
||||
@@ -183,6 +183,7 @@ Dans cette section, on démontre que quelques fonctions élémentaires sont réc
|
||||
> > $\chi _{B}(\overline{x}, z) = \mathrm{sg}\left( \sum\limits_{t=0}^{z} \chi _{A}(\overline{x}, t) \right)$
|
||||
> > et celle de $C$ par :
|
||||
> > $\chi _{C}(\overline{x}, z) = \mathrm{sg}\left( \prod\limits_{t=0}^{z} \chi _{A}(\overline{x}, t) \right)$
|
||||
^cloture-par-quantification-bornee
|
||||
|
||||
## Schémas de définition supplémentaires
|
||||
On peut trouver de nouveaux schémas de définitions de fonctions qui sont stables sur les fonctions récursives primitives.
|
||||
|
||||
@@ -18,18 +18,7 @@ aliases:
|
||||
|
||||
> [!proposition]+ Représentation des suites comme nombres
|
||||
> On peut trouver une [[bijection]] entre $\mathbb{N}$ et l'ensemble des suites finies à $p$ éléments.
|
||||
> De plus, cette bijection est [[fonction récursive primitive|récursive primitive]].
|
||||
> > [!démonstration]+ Démonstration
|
||||
> > On procède en définissant l'application de $\mathscr{S} \to \mathbb{N}$ suivante :
|
||||
> > $\Omega((x_0, x_1, \dots, x_{p})) = \pi(0)^{x_0} \cdot \pi(1)^{x_1} \cdot\cdots \cdot \pi(p)^{x_{p}}$ (voir [[fonction pi|fonction π]])
|
||||
> > On sait par l'arithmétique ([[décomposition en facteurs premiers]]) que cette fonction est bien une bijection.
|
||||
> > Par ailleurs, comme [[fonction pi#^recursive-primitive|la fonction π est récursive primitive]], on sait que $\Omega$ est récursive primitive aussi
|
||||
> > Montrons maintenant que la réciproque de $\Omega$ est également récursive primitive :
|
||||
> > définissons la fonction $\delta \in \mathscr{F}_{2}$ :
|
||||
> > $\delta(i, x) := \mu z \leq x \quad (x \text{ n'est pas divisible par } \pi(i)^{z+1})$
|
||||
> > On sait que [[divisibilité#^recursive-primitive|le prédicat de divisibilité est récursif primitif]], ce qui montre que $\delta$ est récursive primitive.
|
||||
> > Maintenant, la fonction $\lambda x. (\delta(1, x), \delta(2, x), \dots, \delta(p, x))$ est bien la réciproque de $\Omega$
|
||||
> > une ligne super long avec plein de text super long qui va dépasser jusqu'à la fin de la ligne pour pouvoir tester si le symbole bave et
|
||||
> De plus, cette bijection peut être [[fonction récursive primitive|récursive primitive]].
|
||||
|
||||
# Exemples
|
||||
|
||||
|
||||
@@ -0,0 +1,40 @@
|
||||
---
|
||||
up:
|
||||
- "[[suite finies d'entiers]]"
|
||||
- "[[fonction récursive primitive]]"
|
||||
tags:
|
||||
- s/maths/logique
|
||||
- s/informatique
|
||||
aliases:
|
||||
---
|
||||
|
||||
|
||||
> [!proposition]+ Représentation avec des couples
|
||||
> Le but est de trouver une fonction qui fasse l'association entre un nombre et un $p$-uplet (une suite de $p$ entiers).
|
||||
> On veut montrer qu'il existe $\alpha _{p} \in \mathscr{F}_{p}$ et $\beta _{p}^{1}, \beta _{p}^{2}, \dots, \beta _{p}^{p} \in \mathscr{F}_{p}$ telles que $\alpha _{p}$ est une [[bijection]] et que l'application réciproque de $\alpha _{p}$ soit $\lambda x. (\beta _{p}^{1}, \beta _{p}^{2}, \dots, \beta _{p}^{p})$
|
||||
> - **Couples :**
|
||||
> On commence par construire $\alpha _{2}$ pour les couples, dont la réciproque doit être $\lambda x. (\beta _{2}^{1}, \beta _{2}^{2})$ :
|
||||
> Pour cela, on décide d'ordonner les couples d'entiers comme suit :
|
||||
> ![[attachments/ordre sur les couples d'entiers 2026-03-21 18.43.49.excalidraw]]
|
||||
> C'est-à-dire en suivant les diagonales à $x+y$ constant, en commençant par $x+y=0$, puis $x+y=1$ ...
|
||||
> la valeur de $\alpha_2(x, y)$ sera alors le nombre de couples précédant $(x, y)$ dans cette énumération
|
||||
> tes
|
||||
> Considérons le couple $(p, n)$ :
|
||||
> Il se trouve dans la diagonale $p+n$. Les couples avant cette diagonale sont au nombre de $\frac{(p+n)(p+n+1)}{2}$, et le couple $(p, n)$ est le $n^{\text{ème}}$ de sa diagonale.
|
||||
> Cela montre que $\alpha _{2}(p, n) = \frac{1}{2}(p+n)(p+n+1)+n$.
|
||||
> On peut ensuite retrouver $\beta _{2}^{1}$ et $\beta _{2}^{2}$ comme suit (à l'aide de [[schéma mu borné|schémas µ bornés]] et de la [[fonction récursive primitive#^cloture-par-quantification-bornee|clôture par quantification bornée]]) :
|
||||
> - $\beta _{2}^{1} = \mu z \leq x \quad (\exists w\leq x,\quad \alpha_2(z, w) = x)$
|
||||
> - $\beta _{2}^{2} = \mu z \leq x \quad (\exists w\leq x,\quad \alpha_2(w, z) = x)$
|
||||
|
||||
|
||||
> [!proposition]+ Seconde approche
|
||||
> On procède en définissant l'application de $\mathscr{S} \to \mathbb{N}$ suivante :
|
||||
> $\Omega((x_0, x_1, \dots, x_{p})) = \pi(0)^{x_0} \cdot \pi(1)^{x_1} \cdot\cdots \cdot \pi(p)^{x_{p}}$ (voir [[fonction pi|fonction π]])
|
||||
> On profite ici de la [[décomposition en facteurs premiers]].
|
||||
> Par ailleurs, comme [[fonction pi#^recursive-primitive|la fonction π est récursive primitive]], on sait que $\Omega$ est récursive primitive aussi
|
||||
> Montrons maintenant que la réciproque de $\Omega$ est également récursive primitive :
|
||||
> définissons la fonction $\delta \in \mathscr{F}_{2}$ :
|
||||
> $\delta(i, x) := \mu z \leq x \quad (x \text{ n'est pas divisible par } \pi(i)^{z+1})$
|
||||
> On sait que [[divisibilité#^recursive-primitive|le prédicat de divisibilité est récursif primitif]], ce qui montre que $\delta$ est récursive primitive.
|
||||
> La fonction $\lambda x. (\delta(1, x), \delta(2, x), \dots, \delta(p, x))$ est bien la réciproque de $\Omega$
|
||||
> - i Cette approche est moins parfaite car $\Omega$ n'est pas bijective
|
||||
@@ -4,6 +4,34 @@
|
||||
> short mode
|
||||
> ```
|
||||
|
||||
```contributionGraph
|
||||
title: Tasks completed
|
||||
graphType: default
|
||||
dateRangeValue: 180
|
||||
dateRangeType: LATEST_DAYS
|
||||
startOfWeek: 0
|
||||
showCellRuleIndicators: true
|
||||
titleStyle:
|
||||
textAlign: left
|
||||
fontSize: 15px
|
||||
fontWeight: normal
|
||||
dataSource:
|
||||
type: ALL_TASK
|
||||
value: ""
|
||||
dateField:
|
||||
type: FILE_NAME
|
||||
filters:
|
||||
- id: "1774113825001"
|
||||
type: CONTAINS_ANY_TAG
|
||||
value:
|
||||
- "#task"
|
||||
- id: "1774114013540"
|
||||
type: STATUS_IS
|
||||
value: COMPLETED
|
||||
fillTheScreen: false
|
||||
enableMainContainerShadow: false
|
||||
cellStyleRules: []
|
||||
```
|
||||
|
||||
> [!smallquery] Done
|
||||
> ```tasks
|
||||
|
||||
Reference in New Issue
Block a user