Math

Page 1

1.1 Real Numbers

Real numbers are used throughout mathematics, and you should be acquainted with the symbols that represent them.

Lowercase letters a,b,c,x,y.. represent arbitrary real numbers (also called variables) if a and b denote the same real numbers, we write a=b, which is "a is equal to b" and is called an equality. The notion a ≠ b is read "a is not equal to b."

The natural numbers are the usual counting numbers: 1,2,3,4,5....

The whole numbers are the all of the natural numbers as well as zero:.... 0,1,2,3,4,5 (non negative integers)

The integers are whole numbers and opposites of the natural numbers: -2,-1,0,1,2

The natural numbers above are therefore positive integers

The rational numbers are the same numbers, which can be expressed as the quotient of two integers.

The irrational numbers are the real numbers which are not rational. (decimal representations which are non terminating and non repeating)

Zero Factor Theorem: If a⋅b = 0, then either a = 0 or b = 0

We use this often when solving equations with zero on one side. (A product is set equal to ZERO)