Mathematics : Real Numbers : Counting

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Mathematics : Real Numbers


All Continuous Sets of Real Numbers contain an Equal Amount of Numbers

If there exists a bijection between 2 sets, then the 2 sets contain an equal amount of numbers.

For sets $X\equiv[0, 1]$ and $Y\equiv[0,10^6]$ the bijection is $x \cdot 10^6 = y$.

Set of continuous sets can be mapped to some continuous region by some other bijection.