SAT Study Guide/Part 2 - The Math Section/General Numerical Concepts

Number properties
There are several sets of numbers:
 * 1) Counting or Natural numbers are numbers that can be used to count real things: $$\left\{ 1, 2, 3,\dots \right\}\quad$$
 * 2) Integers (including 0) include the natural numbers and their opposites: $$\left\{-3, -2, -1, 0, 1, 2, 3,\dots \right\}\quad$$
 * 3) * Even integers are divisible by 2; you can express even integer as $$2n$$, where $$n$$ is any integer: $$\left\{0, 1, -2, 4, 6, 2,\dots \right\}\quad$$
 * 4) * Odd integers are not divisible by 2; you can express any odd integer as $$2n-1$$, where $$n$$ is any integer: $$\left\{-1, 0, 1, 3, 5, 20,\dots \right\}\quad$$
 * 5) Rational numbers are numbers you can express as a fraction $${a \over b}$$, where $$a$$ and $$b$$ cannot simplify the other: $$\left\{-2, -{1 \over 2}, {3 \over 5}, {7 \over 15}, 5.\overline{31354324},\dots \right\}\quad$$
 * 6) Irrational numbers are non-repeating, non-terminating decimals that you cannot express as a ratio or division of intergers $${a \over b}$$, where $$a$$ and $$b$$ cannot simplify the other: $$\left\{\pi, e, \sqrt{2},\dots \right\}\quad$$
 * 7) Real numbers include all of the above.

Numbers can be prime. That is, they are divisible by themselves and one, only. 1 is not considered a prime number, and 2 is the only even prime number. The first eight prime numbers are: $$\left\{2, 3, 5, 7, 11, 13, 17, 19,\dots \right\}\quad$$