Algebra of sets and git flashcards.

notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json

@@ -129,7 +129,11 @@
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     "graph-non-subgraph.png",
     "lcrs-nodes.png",
-    "binary-tree-nodes.png"
+    "binary-tree-nodes.png",
+    "venn-diagram-union.png",
+    "venn-diagram-intersection.png",
+    "venn-diagram-rel-comp.png",
+    "venn-diagram-abs-comp.png"
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notes/_journal/2024-05-22.md

@@ -6,4 +6,8 @@ title: "2024-05-22"
 - [x] KoL
 - [ ] Sheet Music (10 min.)
 - [ ] Go (1 Life & Death Problem)
-- [ ] Korean (Read 1 Story)
+- [ ] Korean (Read 1 Story)
+
+* Read "Chapter 8. The Trouble with Distributed Systems" in "Designing Data-Intensive Applications".
+* Begin taking notes/creating flashcards on the [[algebra|algebra of sets]].
+* Additional flashcards on git branching.

notes/git/objects.md

@@ -517,6 +517,30 @@ Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Soft
 <!--ID: 1709674569928-->
 END%%
 
+%%ANKI
+Basic
+How many parents does an initial commit have?
+Back: Zero.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1716397645567-->
+END%%
+
+%%ANKI
+Basic
+How many parents does a "normal" commit have?
+Back: One.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1716397645568-->
+END%%
+
+%%ANKI
+Basic
+How many parents does a "merge" commit have?
+Back: Two or more.
+Reference: Scott Chacon, *Pro Git*, Second edition, The Expert’s Voice in Software Development (New York, NY: Apress, 2014).
+<!--ID: 1716397645570-->
+END%%
+
 ## Tags
 
 Tags are (possibly indirect) pointers to a git object. They *usually* point to a commit but aren't required to. There are two types of tags:

notes/set/algebra.md

@@ -0,0 +1,120 @@
+---
+title: Algebra of Sets
+TARGET DECK: Obsidian::STEM
+FILE TAGS: algebra::set set
+tags:
+  - algebra
+  - set
+---
+
+## Overview
+
+The study of the operations of union ($\cup$), intersection ($\cap$), and set difference ($-$), together with the inclusion relation ($\subseteq$), goes by the **algebra of sets**.
+
+%%ANKI
+Basic
+What three operators make up the algebra of sets?
+Back: $\cup$, $\cap$, and $-$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060602-->
+END%%
+
+%%ANKI
+Basic
+What *relation* is relevant in the algebra of sets?
+Back: $\subseteq$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060605-->
+END%%
+
+## Laws
+
+The algebra of sets obey laws reminiscent (but not exactly) of the algebra of real numbers.
+
+%%ANKI
+Cloze
+{$\cup$} is to algebra of sets whereas {$+$} is to algebra of real numbers.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060607-->
+END%%
+
+%%ANKI
+Cloze
+{$\cap$} is to algebra of sets whereas {$\cdot$} is to algebra of real numbers.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060609-->
+END%%
+
+%%ANKI
+Cloze
+{$-$} is to algebra of sets whereas {$-$} is to algebra of real numbers.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060611-->
+END%%
+
+%%ANKI
+Cloze
+{$\subseteq$} is to algebra of sets whereas {$\leq$} is to algebra of real numbers.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060614-->
+END%%
+
+### Commutative Laws
+
+For any sets $A$ and $B$, $$\begin{align*} A \cup B & = B \cup A \\ A \cap B & = B \cap A \end{align*}$$
+
+%%ANKI
+Basic
+The commutative laws of the algebra of sets apply to what operators?
+Back: $\cup$ and $\cap$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060616-->
+END%%
+
+%%ANKI
+Basic
+What does the union commutative law state?
+Back: For any sets $A$ and $B$, $A \cup B = B \cup A$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060618-->
+END%%
+
+%%ANKI
+Basic
+What does the intersection commutative law state?
+Back: For any sets $A$ and $B$, $A \cap B = B \cap A$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060620-->
+END%%
+
+### Associative Laws
+
+For any sets $A$ and $B$, $$\begin{align*} A \cup (B \cup C) & = (A \cup B) \cup C \\ A \cap (B \cap C) & = (A \cap B) \cap C \end{align*}$$
+
+%%ANKI
+Basic
+The associative laws of the algebra of sets apply to what operators?
+Back: $\cup$ and $\cap$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060622-->
+END%%
+
+%%ANKI
+Basic
+What does the union associative law state?
+Back: For any sets $A$, $B$, and $C$, $A \cup (B \cup C) = (A \cup B) \cup C$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060624-->
+END%%
+
+%%ANKI
+Basic
+What does the intersection associative law state?
+Back: For any sets $A$, $B$, and $C$, $A \cap (B \cap C) = (A \cap B) \cap C$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716396060625-->
+END%%
+
+## Bibliography
+
+* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).

notes/set/index.md

@@ -359,6 +359,15 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1715900348153-->
 END%%
 
+%%ANKI
+Basic
+What set operation is shaded green in the following venn diagram?
+![[venn-diagram-union.png]]
+Back: $A \cup B$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245855-->
+END%%
+
 ### General Form
 
 For any set $A$, there exists a set $B$ whose elements are exactly the members of the members of $A$: $$\forall A, \exists B, \forall x, x \in B \Leftrightarrow (\exists b \in B, x \in b)$$
@@ -435,6 +444,54 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1716309007864-->
 END%%
 
+%%ANKI
+Basic
+What kind of mathematical object is the absolute complement of set $A$?
+Back: A class.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245860-->
+END%%
+
+%%ANKI
+Basic
+What kind of mathematical object is the relative complement of set $B$ in $A$?
+Back: A set.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245862-->
+END%%
+
+%%ANKI
+Cloze
+{1:Classes} are to {2:absolute} complements whereas {2:sets} are to {1:relative} complements.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245866-->
+END%%
+
+%%ANKI
+Basic
+What contradiction arises when arguing the absolute complement of set $A$ is a set? 
+Back: The union of the complement with $A$ is the *class* of all sets.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245868-->
+END%%
+
+%%ANKI
+Basic
+Why is the absolute complement of sets rarely useful in set theory?
+Back: The absolute complement of a set isn't a set.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245870-->
+END%%
+
+%%ANKI
+Basic
+What set operation is shaded green in the following venn diagram?
+![[venn-diagram-abs-comp.png]]
+Back: The absolute complement of $A$.
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716397645564-->
+END%%
+
 ## Power Set Axiom
 
 For any set $a$, there is a set whose members are exactly the subsets of $a$: $$\forall a, \exists B, \forall x, (x \in B \Leftrightarrow x \subseteq a)$$
@@ -656,6 +713,24 @@ Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Pre
 <!--ID: 1716309007881-->
 END%%
 
+%%ANKI
+Basic
+What set operation is shaded green in the following venn diagram?
+![[venn-diagram-intersection.png]]
+Back: $A \cap B$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245873-->
+END%%
+
+%%ANKI
+Basic
+What set operation is shaded green in the following venn diagram?
+![[venn-diagram-rel-comp.png]]
+Back: $A - B$
+Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
+<!--ID: 1716395245875-->
+END%%
+
 ## Bibliography
 
 * Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).