# 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: ${\displaystyle \left\{1,2,3,\dots \right\}\quad }$
2. Integers (including 0) include the natural numbers and their opposites: ${\displaystyle \left\{-3,-2,-1,0,1,2,3,\dots \right\}\quad }$
• Even integers are divisible by 2; you can express even integer as ${\displaystyle 2n}$ , where ${\displaystyle n}$  is any integer: ${\displaystyle \left\{0,1,-2,4,6,2,\dots \right\}\quad }$
• Odd integers are not divisible by 2; you can express any odd integer as ${\displaystyle 2n-1}$ , where ${\displaystyle n}$  is any integer: ${\displaystyle \left\{-1,0,1,3,5,20,\dots \right\}\quad }$
3. Rational numbers are numbers you can express as a fraction ${\displaystyle {a \over b}}$ , where ${\displaystyle a}$  and ${\displaystyle b}$  cannot simplify the other: ${\displaystyle \left\{-2,-{1 \over 2},{3 \over 5},{7 \over 15},5.{\overline {31354324}},\dots \right\}\quad }$
4. Irrational numbers are non-repeating, non-terminating decimals that you cannot express as a ratio or division of intergers ${\displaystyle {a \over b}}$ , where ${\displaystyle a}$  and ${\displaystyle b}$  cannot simplify the other: ${\displaystyle \left\{\pi ,e,{\sqrt {2}},\dots \right\}\quad }$
5. 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: ${\displaystyle \left\{2,3,5,7,11,13,17,19,\dots \right\}\quad }$