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types of #
 N Natural numbers
 W Whole numbers
 Z Integers
 Q Rational numbers
 I Irrational numbers
 R Real numbers

natural numbers
 counting numbers
 1, 2, 3
 subset of whole numbers, contained in the set of integers, which is inside the set of rational numbers
 x + 2 = 5 {1, 2, 3, ....

whole numbers
 {0, 1, 2, 3, ...
 natural numbers + 0
 positive numbers
 excludes: fractions, decimals
 subset of integers

integers
 {0, + 1, + 2, + 3...
 whole numbers & negative numbers
 positive numbers + negative numbers + 0

rational numbers
 Q
 integers + fractions + decimals
 includes repeating/terminating decimals: 0.54444
 real # that can be written as ratio of integers c nonzero denom

irrational numbers
 can't be expressed as ratio of 2 numbers
 real numbers that aren't rational
excludes: integers, fractions

real numbers
 rational + irrational numbers;
 natural numbers + whole numbers
 integers
 fractions & decimals

set
 collection of distinct items without repeating
 i.e.: natural #s are subset of integers

proof
means by which math is validated

use summation notation to denote average

prove that adding two even numbers = an even number
 2 variables for even #: x y
 x = 2q q is an element of Z (integer)
 y = 2p p is an element of Z (integer)
 x + y
 2q + 2p = 2 (p + q)
 therefore x + y is even

find formula for adding 1 to n
sum = 1 + 2 + 3+ ... + n
 1 S = 1 + 2 + 3 + ... + (n2) + (n1) + n
 2S = n +(n1) + (n2) + .... 3 + 2 + 1
 1 + n = n + 1
 2 + (n1) = n + 1
 3 + (n2) = n + 1
 ....
 (n2) + 3 = n + 1
 (n1) + 2 = n + 1
 n + 1 = n + 1

identify domain, range, inputs, codomain, & image
 A = inputs
 B = codomain
 A is subset of B
 domain (g) = A
 image: set/collection of all outputs
 image (g) is contained in codomain

