wiki/math/proof/notes.page

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title: Mathematical Proof Study Notes
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# Texts

- *Book of Proof*, Richard Hammack

# Reading Notes

## *Hammack*, 25 Jan 2014

All of Mathematics can be described with *sets*.

*set*
: A collection of things. The things in the set are called *elements*.

An example of a set: $\{2,4,6,8\}$

The set of all integers:
$$ \{\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\} $$

The dots mean the expressed pattern continues.

Sets of infinitely many members are *infinite*, otherwise they are
*finite*.

Sets are *equal* if they have exactly the same elements.

E.g. $\{2,4,5,8\} = \{4,2,8,6\}$ but $\{2,4,6,8\} \neq \{2,4,6,7\}$.

Uppercase letters often denote sets, e.g. $A = \{1,2,3,4\}$.

To express membership, we use $\in$, as in $2 \in A$.