# Why are we not allowed to divide by 0?

## Why are we not allowed to divide by 0?

These notes discuss why we cannot divide by 0. The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1. Arithmetic starts by assuming there are objects called real numbers.

### What happens if you divide by 0?

We know that 0 divided by any number is 0, but we also know that any number divided by 0 is undefined.

Will dividing by 0 ever be defined?

Similarly, to support division of any integer by any other, the realm of numbers must expand to the rational numbers. Loosely speaking, since division by zero has no meaning (is undefined) in the whole number setting, this remains true as the setting expands to the real or even complex numbers.

Is it acceptable to divide by zero True or false?

In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a (assuming a ≠ 0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 00 is also undefined; when it is the form of a limit, it is an indeterminate form.

## Why do some people say 0 divided by 0?

Why some people say it’s 0: Zero divided by any number is 0. Why some people say it’s 1: A number divided by itself is 1. Why some people say it’s undefined: Dividing by zero is undefined. Only one of these explanations is valid, and choosing the other explanations can lead to serious contradictions.

### Is it possible to divide any number by itself?

Rebuttal: Any number divided by itself is 1. 1. 1. Reply: This is true for any nonzero number, but dividing by 0 0 0 is not allowed. Rebuttal: 0 0 0 divided by any number is 0. 0. 0. Reply: This is true for any nonzero denominator, but dividing by 0 0 0 is not allowed no matter what the numerator is.

Can a number be divided by a nonzero number?

1. 1. Reply: This is true for any nonzero number, but dividing by 0 0 0 is not allowed. Rebuttal: 0 0 0 divided by any number is 0. 0. 0. Reply: This is true for any nonzero denominator, but dividing by 0 0 0 is not allowed no matter what the numerator is.

Which is the undefined form of division by zero?

In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a (assuming a ≠ 0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0 0 is also undefined; when it is the form of a limit, it is an indeterminate form.