Mathematical Proof/Appendix/Symbols Used in this Book

< Mathematical Proof < Appendix

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)\}.

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