-
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 non-zero 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 + ... + (n-2) + (n-1) + n
- 2S = n +(n-1) + (n-2) + .... 3 + 2 + 1
- 1 + n = n + 1
- 2 + (n-1) = n + 1
- 3 + (n-2) = n + 1
- ....
- (n-2) + 3 = n + 1
- (n-1) + 2 = n + 1
- n + 1 = n + 1
-
identify domain, range, inputs, co-domain, & image
- A = inputs
- B = co-domain
- A is subset of B
- domain (g) = A
- image: set/collection of all outputs
- image (g) is contained in co-domain
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