Describe how you would approach a proof that two infinite se

Describe how you would approach a proof that two infinite sets have the same cardinality. Examples you might consider include |Z| = |2Z|. |N| = |N_0|. or |(0, 1)|=|R|.

Solution

We approach the problem by creating a bijection between the two sets. Let us assume we have two sets, the first one with all the natural numbers and second one with all even natural numbers. For every number in the first set we map it with twice of that number in the second set. We map 1 -> 2, 2 -> 4 and 3 -> 6 and so on. So as we are able to achieve a bijection, the cardinality of two sets should be same.