# Mathematical Proof/Appendix/Symbols Used in this Book

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

$[a,b]$ Closed interval notation. Signifies the set of all numbers between a and b (a and b included)

$\lor$ 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. $A\cap B=\{x|(x\in A)\land (x\in B)\}.$ 