1. Types of numbers
The set of Natural numbers is denoted by and consists of {1, 2, 3, ..., ∞}
The set of Whole numbers is denoted by W and consists of {0, 1, 2, 3, ..., ∞}
The set of Whole numbers and their additive inverses forms the set of Integers denoted by and consisting of {-∞, ..., -3, -2, -1, 0, 1, 2, 3, ..., ∞}
Any number that can be expressed as $x/y$ where $y≠0$, is called a Rational number. This set of numbers is denoted by
Any non-repeating, non-terminating decimal number or fraction, or transcendental number belongs to the set of Irrational numbers.
The set of all rational and irrational numbers forms the set of Real numbers. This set is denoted by

All positive numbers have square roots defined in the set of real numbers.
The rest of the sets of numbers below are not tested in the GRE, GMAT or SAT, but are included here for completeness.

A set of Imaginary numbers is defined that includes the square roots of negative numbers.
A number that has both real and imaginary parts is called a Complex number. The set of Complex numbers is denoted by

Notes:

Additive inverses are numbers which when added to a number give a result of 0.
e.g. $3+(-3)=0$, so $3$ and $-3$ are the additive inverses of each other.
This is similar in concept to a multiplicative inverse (reciprocal), which is a number when multiplied with a given number gives a result of 1.
e.g. $3*(1/3)=1$, so $3$ and $1/3$ are multiplicative inverses of each other.

The line of numbers extending from -∞ to ∞ is called the number line.
Two perpendicular number lines in a plane define the normal x-y coordinate system we are used to seeing.
The vertical line is called the y-axis while the horizontal one is called the x-axis.
Every point in the plane can be identified by a pair of numbers (called coordinates) denoting its position along the x and y axes.

A coordinate plane where the y axis denotes only imaginary numbers while the x axis counts real numbers, is called the Argand Diagram.
The Argand Diagram can denote Complex numbers in that plane.

 


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