the evolution of numbers

1. The Evolution of
Numbers

2. What is the simplest idea of a number?
Something to count with!

3. The Counting Numbers
Counting Numbers: {1, 2, 3, ...}
And the "Counting Numbers" satisfied people for
a long time...

4. The Whole Numbers
 if there is nothing to count, how can you count it?
The idea of zero was not natural to early
humans ...
 difference between "4" and "40" ? Without
the zero they look the same!

5. The Natural Numbers
• the "Counting Numbers": {1, 2, 3, ...}
• or the "Whole Numbers": {0, 1, 2, 3, ...}
they disagree on whether zero is "natural" or not.

6. Negative Numbers
We can count forwards: 1, 2, 3, 4, ..
... but what if we count backwards:
3, 2, 1, 0, ... what happens next?
If we include the negative numbers with the whole numbers, we
have a new set of numbers that are called integers

7. Int egers
Integers: {..., -3, -2, -1, 0, 1, 2, 3, ...}

8. Fr ac t i ons
If you have one orange and want to
share it with someone, you need to cut it in half.
You have just invented a new type of number!

9. Rational Numbers
• all the integers
• and all fractions.

10. But There Is More...
If you draw a square (of size "1"),
what is the distance across the diagonal?
The answer is the square root of 2, which is
1.4142135623730950...(etc)
.. and it is not a rational number

11. Irrational Numbers

12. Real Num bers
Real Numbers include:
• the rational numbers, and
• the irrational numbers