What is infinity squared?

Answer 1

Infinity squared is infinity. But there's more to it.
Mathematicians describe different kinds of infinities:

• The cardinality(number) of natural numbers is called Aleph0 () . This is infinite, and it has some peculiar properties:

1. The cardinality of even numbers is also Aleph0.
2. As is the cardinality of odd numbers.
3. As is the cardinality of rational numbers (which you could view as infinity squared, but it still gives you infinity.

• The cardinality of countable ordinal numbers is called Aleph1 ().
• The cardinality of the real numbers is two to the exponent of Aleph0 ( ). The continuum hypothesis says this is equal to Aleph1.

Basically, if you square an infinite set from a given cardinality, the cardinality stays the same (meaning Aleph0 squared is still Aleph0, etc.)

If your mind just burst(cause mine did! 0_o), do not worry. This is a common reaction to set theory.

See the related link for more on Aleph numbers, which are how mathematicians view infinity.

Answer 2

6. Infinite square

Infinite squareInfinite square