Real Numbers

Real Numbers are just numbers like:

1 12.38 −0.8625 3/4 √2 198

In fact:

Nearly any number you can think of is a Real Number

Real Numbers include:

  Whole Numbers (like 0, 1, 2, 3, 4, etc)
  Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )
  Irrational Numbers (like π, √3, etc )

Real Numbers can also be positive, negative or zero.

So ... what is NOT a Real Number?

  Imaginary Numbers like √−1 (the square root of minus 1)
are not Real Numbers
  Infinity is not a Real Number

And there are also some special numbers that mathematicians play with that aren't Real Numbers.

Why are they called "Real" Numbers?

Because they are not Imaginary Numbers.

The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!

The Real Number Line

The Real Number Line is like a geometric line.

A point is chosen on the line to be the "origin", points to the right are positive, and points to the left are negative.

Real Number Line

A distance is chosen to be "1", then whole numbers are marked off: {1,2,3,...}, and also in the negative direction: {−1,−2,−3, ...}

Any point on the line is a Real Number:

  • The numbers could be whole (like 7)
  • or rational (like 20/9)
  • or irrational (like π)

But you won't find Infinity, or an Imaginary Number.

Real does not mean they are in the real world


They are not called "Real" because they show the value of something real.

In mathematics we like our numbers pure, when we write 0.5 we mean exactly half.

But in the real world half may not be exact (try cutting an apple exactly in half).