37 lines
760 B
Plaintext
37 lines
760 B
Plaintext
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---
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format: markdown
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toc: yes
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title: Mathematical Proof Study Notes
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...
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# Texts
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- *Book of Proof*, Richard Hammack
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# Reading Notes
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## *Hammack*, 25 Jan 2014
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All of Mathematics can be described with sets.
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*set*
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: A collection of things. The things in the set are called *elements*.
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An example of a set: ${2,4,6,8}$
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The set of all integers:
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$$ {\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots} $$
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The dots mean the expressed pattern continues.
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Sets of infinitely many members are *infinite*, otherwise they are
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*finite*.
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Sets are *equal* if they have exactly the same elements.
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E.g. ${2,4,5,8} = {4,2,8,6}$ but ${2,4,6,8} \neq {2,4,6,7}$.
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Uppercase letters often denote sets, e.g. $A = {1,2,3,4}$.
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To express membership, we use $\in$, as in $2 \in A$.
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