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