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