Real Numbers
Real Numbers are just numbers like:
In fact:
Nearly any number you can think of is a Real Number
Real Numbers include:
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Integers (... −3, −2, −1, 0, 1, 2, 3, ...) | |
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Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, and so on ) | |
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Irrational Numbers (like π, √2, and so on ) |
Real Numbers can be positive, negative or zero.
So ... what's NOT a Real Number?
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Imaginary Numbers (like √−1 the square root of minus 1) aren't Real Numbers |
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Infinity isn't 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 right are positive, and points left are negative.
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:
- The numbers could be whole (like 7)
- or rational (like 20/9)
- or irrational (like π)
But we won't find Infinity, or an Imaginary Number.
Try it here, or try the Zoomable Number Line:
Any Number of Digits
A Real Number can have any number of digits either side of the decimal point
- 120
- 0.12345
- 12.5509
- 0.000 000 0001
There can be an infinite number of digits, such as 13 = 0.333...
Why are they called "Real" Numbers?
Because they aren't Imaginary Numbers
The Real Numbers had no name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That's the actual answer!
Real doesn't 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).