Wednesday, May 15, 2019

elementary set theory - Infinite decimals to prove that intervals are equipotent

Use infinite decimals to prove that the real interval(0,10) is equipotent to its subset, (0,1).


I've deduced through infinite decimals that the interval (0,1) is uncountable, but I'm unsure how to prove that it is as uncountable as the interval (0,10). Can I just say that (0,1) $\subset$ (0,10), thus (0,10) is also uncountable, but this does not prove they're equipotent?

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