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The continuum is the set of real numbers.



The continuum hypothesis claims at a glance:

There is no set whose cardinality lies between the cardinality of the integers and the cardinality of the real numbers.

You can write that as

The smallest cardinal number, for the countably infinite set of integers, is defined as

The second cardinal number, for the uncountable infinite set of real numbers, you can then define as

You can't prove this hypothesis.


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