diff --git a/math/proof/notes.page b/math/proof/notes.page index ba2597b..908dea4 100644 --- a/math/proof/notes.page +++ b/math/proof/notes.page @@ -12,15 +12,15 @@ title: Mathematical Proof Study Notes ## *Hammack*, 25 Jan 2014 -All of Mathematics can be described with sets. +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: ${2,4,6,8}$ +An example of a set: $\{2,4,6,8\}$ The set of all integers: -$$ {\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots} $$ +$$ \{\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\} $$ The dots mean the expressed pattern continues. @@ -29,8 +29,8 @@ Sets of infinitely many members are *infinite*, otherwise they are Sets are *equal* if they have exactly the same elements. -E.g. ${2,4,5,8} = {4,2,8,6}$ but ${2,4,6,8} \neq {2,4,6,7}$. +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. $A = {1,2,3,4}$. +Uppercase letters often denote sets, e.g. $A = \{1,2,3,4\}$. To express membership, we use $\in$, as in $2 \in A$.