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eduroam-prg-og-1-29-184.net.univ-paris-diderot.fr 2026-3-23:9:44:47

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oskar
2026-03-23 09:44:47 +01:00
parent 3dfb5305ca
commit 1de2d5e478
2 changed files with 12 additions and 4 deletions
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4
.obsidian/plugins/breadcrumbs/data.json vendored
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@@ -631,7 +631,7 @@
"prevs" "prevs"
], ],
"lock_view": false, "lock_view": false,
"lock_path": "fonction d'ackermann de cori et lascar.md" "lock_path": "anneau.md"
}, },
"tree": { "tree": {
"collapse": false, "collapse": false,
@@ -651,7 +651,7 @@
"alias": false "alias": false
}, },
"lock_view": false, "lock_view": false,
"lock_path": "fonction d'ackermann de cori et lascar.md" "lock_path": "anneau.md"
} }
}, },
"codeblocks": { "codeblocks": {

12
anneau.md
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@@ -24,10 +24,10 @@ aliases:
```breadcrumbs ```breadcrumbs
title: "Sous-notes" title: "Sous-notes"
type: tree type: tree
collapse: false collapse: true
show-attributes: [field] show-attributes: [field]
field-groups: [downs] field-groups: [downs]
depth: [0, 0] depth: [0, 2]
``` ```
# Propriétés # Propriétés
@@ -41,5 +41,13 @@ depth: [0, 0]
> > $a0_{A} = a(0_{A} + 0_{A}) = a0_{A} + a 0_{A}$ > > $a0_{A} = a(0_{A} + 0_{A}) = a0_{A} + a 0_{A}$
> > d'où suite que $a 0_{A} = 0_{A}$ > > d'où suite que $a 0_{A} = 0_{A}$
> [!proposition]+ Distributivité généralisée
> Soient $m, n \in \mathbb{N}^{*}$
> Soient $(a_1, \dots, a_{n}) \in A^{n}$ et $(b_1, \dots, b_{n}) \in A^{n}$
> On a :
> $\left( \sum\limits_{i=1}^{m} a_{i}\right) \times \left( \sum\limits_{j=1}^{n}b_{j} \right) = \sum\limits_{i=1}^{m}\sum\limits_{j=1}^{n}(a_{i}b_{j})$
> > [!démonstration]- Démonstration
> > La démonstration se fait par double récurrence sur $m$ et sur $n$
# Exemples # Exemples