Much Ado About Nothing
Have you ever thought about what we mean by “division by zero”? First we must divide what we mean by “division”. For instance, how might the question “8 ÷ 2 = ?” arise?
- If 8 biscuits are shared between 2 people, how many will each person have?
- If 8 metres of string is cut into 2 equal pieces, how long will each piece be?
- If 8 metres of string is cut into 2 metre lengths, how many pieces will there be?
Now let’s look at what happens to these questions when we replace the number 2 by 0.
Questions 1. and 2. become total nonsense. You cannot even begin to give biscuits to 0 people. One piece of string can never become 0 pieces of string.
Question 3. is different. When we divided 8m into 2m lengths we are really counting how many times we can subtract 2m from 8m before we run out of string. If we now try dividing 8m into 0m lengths in the same way, we discover that we can subtract 0m from 8m over and over and over again. We will never run out of string.
Do we conclude that division by zero is impossible or do we regard the answer as infinite – I wonder?
