Give an example of proper subset of N that has the same cardinality as N
If A and B are finite, then A≈B if and only if A and B have the same number of elements.
This example shows that the definition of "same size'' extends the usual meaning for finite sets, something that we should require of any reasonable definition.
We say a set A is countably infinite if N≈A, that is, A has the same cardinality as the natural numbers. We say A is countable if it is finite or countably infinite.
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