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Cardinality

The cardinality is the size of a set.

 


Aleph 0

The smalles cardinal number 0א, for the countably infinite set of the natural numbers, is defined as

and is = the set of integers = the set of rational numbers = the set of algebraic numbers.

 


Aleph 1

The next cardinal number 1א, for the uncountable infinite set of real numbers, is defined as

and if we assume the continuum hypothesis, then it is = the set of transcendental numbers = the set of complex numbers = the number of points on a line = the number of points on a line segment = the number of points in the universe.

 


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