37 lines
776 B
Plaintext
37 lines
776 B
Plaintext
---
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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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