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Daily notes.

c-declarations
Joshua Potter 2024-07-01 08:34:35 -06:00
parent d74f149d92
commit 6cd8e0a2ca
6 changed files with 30 additions and 10 deletions
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notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json
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"Basic": [

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---
title: "2024-06-30"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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@ -0,0 +1,9 @@
---
title: "2024-07-01"
---
- [x] Anki Flashcards
- [x] KoL
- [x] OGS
- [ ] Sheet Music (10 min.)
- [ ] Korean (Read 1 Story)

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notes/set/functions.md
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%%ANKI
Basic
Let $F \colon A \rightarrow B$. *Why* does "left inverses iff injective" require $A \neq \varnothing$?
Back: Because a mapping from $B$ to $\varnothing$ cannot be a function.
Let $F \colon A \rightarrow B$. *Why* does "left inverses iff injective" assume $A \neq \varnothing$?
Back: Because a mapping from nonempty $B$ to $\varnothing$ cannot be a function.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719683703729-->
END%%
@ -600,8 +600,8 @@ END%%
%%ANKI
Basic
Let $F \colon A \rightarrow B$. *Why* does "right inverses iff surjective" require $A \neq \varnothing$?
Back: Because a mapping from $B$ to $\varnothing$ cannot be a function.
Let $F \colon A \rightarrow B$. *Why* does "right inverses iff surjective" assume $A \neq \varnothing$?
Back: Because a mapping from nonempty $B$ to $\varnothing$ cannot be a function.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719683703734-->
END%%
@ -1002,14 +1002,14 @@ END%%
%%ANKI
Cloze
Let $F$ be {a function}. If $t \in$ {$\mathop{\text{ran}}F$}, then $F(F^{-1}(t)) = t$.
Let $F$ be a {function}. If $t \in$ {$\mathop{\text{ran} }F$}, then $F(F^{-1}(t)) = t$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756562-->
END%%
%%ANKI
Cloze
Let $F$ be {an injection}. If $t \in$ {$\mathop{\text{dom}}F$}, then $F^{-1}(F(t)) = t$.
Let $F$ be an {injection}. If $t \in$ {$\mathop{\text{dom} }F$}, then $F^{-1}(F(t)) = t$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1719398756565-->
END%%

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notes/set/relations.md
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@ -390,7 +390,7 @@ END%%
%%ANKI
Basic
What does it mean for a set $A$ to be "single-rooted"?
Back: For each $y \in \mathop{\text{ran}}A$, there exists a unique $x$ such that $xRy$.
Back: For each $y \in \mathop{\text{ran}}A$, there exists a unique $x$ such that $xAy$.
Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
<!--ID: 1718465870483-->
END%%