Division by zero is a definite no-no whenever you’re doing math. It simply doesn’t make any sense from an arithmetic standpoint as there is no possible number which can output the numerator when multiplied by zero. So, when something is divided by zero, mathematicians simply state that the answer is ‘undefined’. This is not a totally abstract idea as you can see it in action in the real world. Computer programmers who accidentally divide by zero will get their code stuck in an infinite loop, for instance. But perhaps the most spectacular illustration of undefined division by zero is to try it on a mechanical calculator.
Youtube user MultiGlizda did it on a Facit ESA-01, an ancient but very sophisticated machine as far as mechanical calculators go. It works on a pin-wheel mechanism and can output answers as long as 13 digits. It sold from 1949 through 1952 by Swedish company Facit Calculators.
Why division by zero is undefined
Division by zero is a disallowed operation because you can not find an answer. For instance:
12 divided by 6 is 2 because
6 times 2 is 12
12 divided by 0 is x would mean that
0 times x = 12
There is no possible number 'x' which multiplied by 0, which is nothing, can output 12, which is something.
If you’re still confused, let’s get back to the basics. Both multiplication and division are nothing more than sequential addition and subtraction, respectively. For instance, 12 divided by 6 can be written as:
12-6 = 6
6-6 = 0
It took two steps, so the answer is two. Likewise, 10 divided by 2 is:
10-2 = 8
8-2 = 6
6-2 = 4
4-2 = 2
2-2 = 0
That's five steps, so the correct answer is 5.
However, 10 divided by zero would look like:
10-0 = 10
10-0 = 10
Check out this more in-depth explanation for why the answer to division by zero is undefined.