What Comes After Infinity?

What comes after infinity?

One might think counting past infinity would require multiplying infinity by two. That is wrong. Infinity multiplied by two is, infinity. Then how do you count past infinity? Well, first, before explaining how to count past infinity, you need to know what a cardinal number is.

A cardinal number is a number that can be used to describe the amount of something. This is how we normally use numbers. If I have four apples, the cardinal number for the set is, four. The set can be described as having a cardinality of four. The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and anything you can count to after that,  can be used as cardinals.

Infinity can not be a cardinal number, because you can always add one to a cardinal number to make it larger.

However, to find infinity, you would need to count all of the different numbers that can be used as cardinals. This infinity is called aleph null (or aleph naught/aleph zero.)

Aleph null, can also be described as the amount of multiples of 2, 3, 4, 5, etc, since there is an infinite number of these multiples.

Although infinity plus one is infinity, a question remains. What would you label the number that you added after infinity on an number line? If there are infinite numbers, and you add one, what would come next? Omega. The number after infinity is an ordinal number called omega.  An ordinal number is a number that describes the order of something, like ‘first’, ‘second’ or ‘third’.

After omega, is omega plus one, omega plus two, and omega plus three. These are all ordinal numbers.

Omega squared, squared, squared, etc, will eventually create another form of infinity known as epsilon naught.

After this comes omega one, aleth omega, and aleth omega squared. The list can go on forever, thus creating another infinity.

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