From cbca6f018b5b4abb7ad9163b7399080bb380ced7 Mon Sep 17 00:00:00 2001 From: Joshua Potter Date: Sat, 17 Feb 2024 17:56:55 -0700 Subject: [PATCH] Additive and multiplicative principles. --- .../plugins/obsidian-to-anki-plugin/data.json | 5 +- notes/_journal/2024-02-17.md | 14 ++- notes/combinatorics/index.md | 89 +++++++++++++++++++ 3 files changed, 103 insertions(+), 5 deletions(-) create mode 100644 notes/combinatorics/index.md diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 091c557..558f34e 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -165,9 +165,10 @@ "algebra/floor-ceiling.md": "456fa31bedb9ec7c2fa1d6f75db81dec", "algebra/index.md": "90b842eb694938d87c7c68779a5cacd1", "algorithms/binary-search.md": "08cb6dc2dfb204a665d8e8333def20ca", - "_journal/2024-02-17.md": "7c71a5ccb5b2f45cb93ef6c485e7b567", + "_journal/2024-02-17.md": "0fad7bf64837646e1018885504d40f41", "_journal/2024-02/2024-02-16.md": "e701902e369ec53098fc2deed4ec14fd", - "binary/integer-encoding.md": "a2c8c83a20f1124fd5af0f3c23894284" + "binary/integer-encoding.md": "a2c8c83a20f1124fd5af0f3c23894284", + "combinatorics/index.md": "c5b005bdce7ab01facfd614b00938ef2" }, "fields_dict": { "Basic": [ diff --git a/notes/_journal/2024-02-17.md b/notes/_journal/2024-02-17.md index 640b003..71038e5 100644 --- a/notes/_journal/2024-02-17.md +++ b/notes/_journal/2024-02-17.md @@ -5,11 +5,19 @@ title: "2024-02-17" - [x] Anki Flashcards - [x] KoL - [ ] Sheet Music (10 min.) -- [ ] OGS (1 Life & Death Problem) -- [ ] Korean (Read 1 Story) +- [x] OGS (1 Life & Death Problem) +- [x] Korean (Read 1 Story) - [ ] Interview Prep (1 Practice Problem) - [ ] Log Work Hours (Max 3 hours) * Began working through two's-complement and unsigned encoding. * Also added more notes on propositional logic. - * Taking a step back from "Concrete Mathematics" to first read through "Discrete Mathematics: An Open Introduction". \ No newline at end of file + * Taking a step back from "Concrete Mathematics" to first read through "Discrete Mathematics: An Open Introduction". +* 101weiqi problems (serial numbers) + * Q-14584 + * Q-253960 + * Q-21834 + * Q-349936 + * Q-9812 +* Read 금도끼와 은도끼 (The Golden Ax and the Silver Ax). +* Read through first section of "Discrete Mathematics: An Open Introduction". Add combinatorics notes. \ No newline at end of file diff --git a/notes/combinatorics/index.md b/notes/combinatorics/index.md new file mode 100644 index 0000000..0785cde --- /dev/null +++ b/notes/combinatorics/index.md @@ -0,0 +1,89 @@ +--- +title: Combinatorics +TARGET DECK: Obsidian::STEM +FILE TAGS: combinatorics set +tags: + - combinatorics + - set +--- + +## Overview + +The **additive principle** states that two finite and disjoint sets $A$ and $B$ satisfy $$|A \cup B| = |A| + |B|$$ + +The **multiplicative principle** states that two finite sets $A$ and $B$ satisfy $$|A \times B| = |A| \cdot |B|$$ + +%%ANKI +Basic +What does the additive principle state? +Back: Given finite and disjoint sets $A$ and $B$, $|A \cup B| = |A| + |B|$. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +What does the multiplicative principle state? +Back: Given finite sets $A$ and $B$, $|A \times B| = |A| \cdot |B|$. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +The additive property applies to sets exhibiting what two properties? +Back: Finiteness and disjointedness. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +The multiplicative property applies to sets exhibiting what property? +Back: Finiteness. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Cloze +The additive principle is to {$\cup$} whereas the multiplicative principle is to {$\times$}. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +If $A$ is finite, how is $A \times B$ rewritten as $|A|$ disjoint sets? +Back: Given $A = \{a_1, \ldots, a_n\}$, $(\{a_1\} \times B) \cup \cdots \cup (\{a_n\} \times B)$. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +If $B$ is finite, how is $A \times B$ rewritten as $|B|$ disjoint sets? +Back: Given $B = \{b_1, \ldots, b_n\}$, $(A \times \{b_1\}) \cup \cdots \cup (A \times \{b_n\})$. +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +How do we denote $A$ and $B$ are disjoint using standard set notation? +Back: $A \cap B = \varnothing$ +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +%%ANKI +Basic +How is the cartesian product $A \times B$ defined? +Back: $A \times B = \{\langle x, y \rangle : x \in A \land y \in B\}$ +Reference: Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). + +END%% + +## References + +* Oscar Levin, _Discrete Mathematics: An Open Introduction_, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). \ No newline at end of file