# Why you can't divide by zero

I've always been wondering why dividing by zero is considered undefined. My intuitive answer would have always been "infinity" or "zero". I just had a discussion about this with a collegue who happens to have a degree in mathematics, and the way they explained it made it absolutely clear why it doesn't make sense to divide by zero.

## Inverse Operations

Before understanding why dividing by zero is undefined, you first need to know about inverse operations. It's quite simple!

An example: `3 + 2 = 5`

. The inverse of addition is *subtraction*, so the inverse of this equation is `5 - 2 = 3`

or `5 - 3 = 2`

.

The same applies to multiplication. The inverse of multiplation is *division*. So the inverse of `6 * 2 = 12`

is `12 / 2 = 6`

or `12 / 6 = 2`

.

## Dividing by zero

Let's try to apply the inverse rule to the number zero, starting with addition. If `2 + 0 = 2`

, then `2 - 0 = 2`

.

But if we have `2 * 0 = 0`

, the inverse of that would be `0 / 0 = 2`

, which is just not true.

Dividing by zero breaks some fundamental laws of mathematics, which is why there's a general consensus that any equasion dividing by zero has no valid answer.

This is post 090 of #100DaysToOffload.