Real Numbers

Real Numbers are just numbers like:

1 12.38 −0.8625 34 π (pi) 198

In fact:

Nearly any number you can think of is a Real Number

Real Numbers include:

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

Real Numbers can also be positive, negative or zero.

So ... what is NOT a Real Number?

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

Mathematicians also play with some special numbers that aren't Real Numbers.

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 with examples

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

Any point on the line is a Real Number:

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

Any Number of Digits

A Real Number can have any number of digits either side of the decimal point

There can be an infinite number of digits, such as 13 = 0.333...

Why are they called "Real" Numbers?

Because they are not Imaginary Numbers

The Real Numbers had no name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!

Real does not mean they are in the real world

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

apple and half

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).


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