Wednesday, January 30, 2019

discrete mathematics - Proving (0,1) and [0,1] have the same cardinality

Prove (0,1) and [0,1] have the same cardinality.



I've seen questions similar to this but I'm still having trouble. I know that for 2 sets to have the same cardinality there must exist a bijection function from one set to the other. I think I can create a bijection function from (0,1) to [0,1], but I'm not sure how the opposite. I'm having trouble creating a function that makes [0,1] to (0,1). Best I can think of would be something like x2.



Help would be great.

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