Are infinities infinite?

Yes. The set of integers is infinite. The set of real numbers between each pair of consecutive integers is infinite. Since there is an infinite number of consecutive integers there will be an infinite number of infinities…of different ‘sizes’.

How many infinities are in infinity?

Odd numbers and even numbers: two infinities in an infinity. Multiples of three, numbers that are one more than a multiple of three, numbers that are one less than a multiple of three: three infinities in an infinity. See how you can fit infinities in an infinity.

Do actual infinities exist?

In the context of a number system, in which “infinity” would mean something one can treat like a number. In this context, infinity does not exist. So there does not exist any one single “infinity” concept; instead, there exists a whole collection of things called “infinite cardinal numbers”.

Are all infinities equal?

Infinite sets are not all created equal, however. There are actually many different sizes or levels of infinity; some infinite sets are vastly larger than other infinite sets. The theory of infinite sets was developed in the late nineteenth century by the brilliant mathematician Georg Cantor.

How are some infinities larger than others?

If you’re given an infinite set, there is a simple method to make a larger infinity: take its power set, which is always of higher cardinality. So not only some infinities are larger than others, but there is no a “largest” inifinity, you can always create a larger one.

Can some infinities be larger than others?

Yes. If you’re given an infinite set, there is a simple method to make a larger infinity: take its power set, which is always of higher cardinality. So not only some infinities are larger than others, but there is no a “largest” inifinity, you can always create a larger one.

Can infinity grow?

Infinity does not grow Infinity is not “getting larger”, it is already fully formed. But infinity does not do anything, it just is.

Can you have bigger infinities?

Sets that have the same size as the set of natural numbers are called ‘countably infinite’. There is more than one ‘infinity’—in fact, there are infinitely-many infinities, each one larger than before!