What is infinity times infinity?

Infinity times infinity is not a well-defined mathematical operation because infinity is not a specific number, but rather a concept representing something that is unbounded or endless. This means that multiplying infinity by infinity does not have a unique answer.

In mathematics, infinity can be considered as a limit that can approach different magnitudes depending on the context. For example, the concept of countable infinity in set theory represents an infinite number of elements that can be put into a one-to-one correspondence with the natural numbers.

When discussing infinity times infinity, it may refer to the cardinality of the set of real numbers, which is the same as the cardinality of the set of natural numbers. This is known as the continuum hypothesis and is often represented as the cardinality of the power set of the natural numbers.

Overall, infinity times infinity is a concept that is explored in philosophy, theoretical mathematics, and set theory, but it does not have a well-defined numerical value.