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what happens when you divide by zero
What is twelve divided by zero? Many people say infinity, some say zero. Neither is right. There is no answer at all, and mathematicians call it undefined.
Why? Division is multiplication run backwards. Twelve divided by three is four, because four times three is twelve. So twelve divided by zero would need a number times zero that makes twelve.
So try some guesses. Zero times zero is zero. Five times zero is zero. A thousand times zero is zero. Every guess lands on zero, so nothing can ever make twelve.
Zero divided by zero is stranger. Now the question is what number times zero makes zero, and every number works. With a million answers and no way to choose, we call it indeterminate.
So where does the infinity idea come from? Picture one divided by x as x shrinks toward zero from the right. One over a tenth is ten, over a hundredth is a hundred, over a thousandth is a thousand.
But come from the left, with x slightly below zero, and the answers plunge: minus ten, minus a hundred, minus a thousand. Up on one side, down on the other, so no single value fits.
The whole story: twelve divided by zero has no number that fits, zero divided by zero has too many, and infinity is only what a shrinking denominator heads toward, never a value.
Computers face the same wall. Many programs stop with an error, and others return a special flag value, called infinity or not-a-number, so you know something broke.
Dividing by zero is not a number too big to write down; it is a question with no answer.