What is 0 divided by 0?

0 divided by 0 is undefined in mathematics.

Division by 0 is undefined because there is no consistent, meaningful result when attempting to divide any number, including 0, by 0. It leads to an indeterminate form, creating ambiguity and violating fundamental mathematical principles. Therefore, mathematicians refrain from performing such operations, and expressions like “0 divided by 0” lack a valid numerical value.

To elaborate, let’s consider the expression ​. Intuitively, if you have nothing (0) and attempt to divide it into zero parts, there is no clear or unique answer. The result could be any number, and this lack of specificity renders the expression undefined.

The concept of division by 0 is crucial in preventing mathematical errors and ensuring the consistency and validity of mathematical operations. In various mathematical contexts, encountering division by zero prompts the declaration of an undefined or indeterminate result.