Nothing becomes a number
Zero as a number
A void with no name
For thousands of years the number line started at 1. You have 5 apples and give all 5 away. You have a void: no apples. But there was no number for that.
You give away all 5 apples. What number tells how many are left?
What this lesson covers
The idea
Zero is defined as the result of subtracting a number from itself: a – a = 0.
A void with no name
For thousands of years the number line started at 1. You have 5 apples and give all 5 away. You have a void: no apples. But there was no number for that.
You give away all 5 apples. What number tells how many are left?
- There is no such number
- A new number, 0
- 5
Give them all away
Pick a number of apples with + and −. Then give them all away, one by one. Do it for 3 different numbers.
a − a = 0
Brahmagupta (628 CE) defined zero as the result of subtracting a number from itself: a − a = 0.
It works for every number: 5 − 5 = 0, 8 − 8 = 0, 100 − 100 = 0. Zero is not just an empty space on the page. It is a number you can compute with.
Notes
Zero is the result of subtracting a number from itself: a − a = 0.
Check yourself
Which subtraction gives zero?
You have 17 sweets and eat them all. 17 − ? = 0. What goes in the box?
Answer: 17
17 − 17 = 0. To get zero you take away the same number you started with.
The Babylonians and the Mayans had a symbol for an empty column. Why was it not yet the number zero?
- 9 − 0. 9 − 0 = 9. Taking away nothing leaves everything.
- 9 − 1. 9 − 1 = 8, not 0.
- 9 − 9 — correct. Yes. a − a = 0, so 9 − 9 = 0.
- It was only a placeholder: they could not add, subtract or multiply with it — correct. Yes. Zero became a number when Brahmagupta gave it rules.
- It was too small to see. Size has nothing to do with it. A number needs rules for adding, subtracting and multiplying.
- They did not write in columns. They did: the symbol marked an empty column. But it was not a number to compute with.