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More than infinity

There are infinitely many degrees of infinity.

 


Investigation

Infinity is not a number with a fixed value, but offers the possibility to continue counting forever. If the elements of an infinite set can be numbered, you call this countably infinite. The amount of natural numbers is countable. This smallest cardinal number is described with the symbol 0א and is called Aleph 0. Aleph is the first letter of the Hebrew alphabet. You can therefore write

Card N = 0א

The set of real numbers is greater than the set of natural numbers. That's why this infinite set is called uncountably infinite. So

Card R > 0א

In general you can make 2n variations with with n elements. Where 2n > n. This also applies to the countably infinite quantity of the natural numbers, so

This larger cardinal number is 1א and is called Aleph 1. Because you can make variations with that also, you get ever larger cardinal numbers

There are infinitely many degrees of infinity – incomprehensible.

 


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