What is infinity squared times two?

Answer 1

It is still infinity.

If you add an infinite number plus a finite number, you get the same infinite number.

If you multiply an infinite number times a finite number, you get the same infinite number.

If you raise an infinite number to a finite power, you get the same infinite number.

For example, aleph-zero squared is still aleph-zero.

If you raise two (or a higher finite number) to an infinite power, you get a larger infinite number. To say it another way, the infinite number must be in the exponent, to get a larger infinity. For example, two to the power aleph-zero is equal to aleph-one; two to the power aleph-one is equal to aleph-two, etc.

Read the Wikipedia article on "Aleph number" for more details. http://en.wikipedia.org/wiki/Aleph_number

Also note that "infinity" has different meanings in different contexts, even if you concentrate only on mathematical meanings (as opposed to philosophical meanings, for example). I therefore suggest you also read articles about "Infinity", for example, at http://en.wikipedia.org/wiki/Infinity