Can an Infinite Set Be Equivalent to Its Proper Subset?

Explanation

True. This is one of the most striking properties of infinite sets — and it is impossible for finite sets. Example: \(\mathbb{N} \sim M\) where \(M = \{2, 4, 6, 8, \ldots\}\) is a proper subset of \(\mathbb{N}\). The bijection \(f(n) = 2n\) witnesses this. In fact, this property is used as an alternative definition of an infinite set.