The **real numbers** are the numbers that can be written in decimal notation, including those that require an infinite decimal expansion. The set of real numbers includes all integers, positive and negative; all fractions; and the irrational numbers those with decimal expansion that never repeat.

An example of an irrational number is **√2**.

**Intervals**

**Intervals** are some set of real numbers.

Closed Interval: [a,b] is a set of numbers x where x is greater than or equal to a and less than or equal to b

Open Interval: (a,b) is a set of numbers x where x is greater than a and less than b

Half open Interval (a,b] is a set of numbers x where x is greater than a and less than or equal to b and [a,b) is a set of numbers x where x is greater than or equal to a and less than b.

Infinite Interval [a, +∞) is a set of numbers x where a is less than or equal to x for example.

**Operations**

There are five important operations for real numbers: addition, subtraction, multiplication, division, and exponentiation.

PEMDAS is the standard order of operations when evaluation equations and stands for parenthesis, exponentiation, division, addition, and subtraction

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