Real numbers are **any numbers that can be represented on the number line.**

The set of real numbers (also called the

*reals*) includes both the set of

**rational numbers**(numbers that can be written as ratios or fractions) and the set of

**irrational numbers**(numbers that can’t be written as fractions, like

*pi*).

There are an **infinite number of reals**, and there is an infinite number of real numbers between any two real numbers. For example, between 1 and 2 there are 0.1, 0.21, 0.239, and so on.

All **whole numbers **(1,2,3,4…) and integers (-2098, -2, 1, 2…) are also included in the set of reals.

The set of reals is denoted by the symbol ℝ.

## What Number is Not a Real Number?

Imaginary numbers of the from a+ib, with i= √(-1) and b ≠ 0, are not reals.

## Core Properties of Real Numbers.

Since every real number has its own place along the number line, reals can be ordered. Properties of real numbers include:

- The Distributive Property: a(b+c)= ab +ac for every a, b, and c in ℝ.
- The Commutative Property: ab=ba and a+b =b+a for a and b in ℝ.
- The Associative Property: (ab)c=a(bc) and (a+b)+c=a+(b+c) for all a, b, and c in ℝ
- The Closure Property: a+b, a-b, and ab are all reals if a and b are real numbers; that is to say, real numbers are closed under addition, subtraction, and multiplication.

## The Identity Properties of Real Numbers

There is one multiplicative identity, 1, and one additive identity, 0, such that

1a= a and 0+a =a

for every a in ℝ.

## The Inverse Properties of Reals

Every real number a has an unique additive inverse –a such that a + (-a) =0, with –a being a member of the set of real numbers. Every nonzero real number a also has a unique multiplicative inverse 1/a such that a(1/a)=1, where 1/a is a real number.

Sources:

http://amsi.org.au/teacher_modules/Real_numbers.html

https://math.vanderbilt.edu/schectex/courses/thereals/

http://mathworld.wolfram.com/RealNumber.html

https://www.math.uh.edu/~charles/Real-nos.pdf

If you prefer an online interactive environment to learn R and statistics, this *free R Tutorial by Datacamp* is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try *this Statistics with R track*.

*Facebook page*and I'll do my best to help!