What is infinity divided by infinity?

Infinity divided by infinity is technically undefined in mathematics because infinity is not a number, but rather a concept representing something that has no limits. It can be thought of as a limit where both the numerator and denominator approach infinity, but the result can vary depending on the context in which it is used.

In practice, dividing infinity by infinity can result in various values, such as 1, 0, or even infinity itself, depending on the specific limits of the sequences being divided. This indeterminacy is one reason why mathematicians typically avoid dividing infinity by infinity and instead use more precise methods to evaluate limits involving infinity.