# Mathematical Proof/Appendix/Symbols Used in this Book

This is a list of all the mathematical symbols used in this book.

$[a,b]$

Interval notation. Signifies the set of all numbers between a and b

$\lor$

A logical "or" connector. A truth statement whose truth value is true if either of the two given statements is true and false if they are both false. $P\lor Q$

$\land$

A logical "and" connector. A truth statement whose truth value is true only if both of the two given statements is true and false otherwise. $P\land Q$

$\lnot$

A logical "not" unary operator. A truth statement whose value is opposite of the given statement. $\lnot P$

{ }

Set delimiters. A set may be defined explicitly (e.g. $A = \{1,2,3,4\}$), or pseudo-explicitly by giving a pattern (e.g. $B = \{2,4,6,8,\ldots\}$. It may also be defined with a given rule (e.g. $C = \{ x | P(x)\}$, the set of all x such that P(x) is true).

$\in$

The "element of" binary operator. This shows element inclusion in a set. If x is an element of A we write $x\in A.$

$\subset$

The "set inclusion" or "subset" binary operator. If all the elements of A are in B, then we say that A is a subset of B and write $A\subset B.$ Note that in this book, $A\subset B$ when $A=B.$

$\cup$

The union of two sets. A set containing all elements of two given sets. $A\cup B = \{x|(x\in A) \lor (x\in B)\}.$

$\cap$

The intersection of two sets. A set containing all the elements that are in both of two given sets. $A\cap B = \{x|(x\in A)\land (x\in B)\}.$