Can a Finite Set Be Equivalent to Its Proper Subset?

Explanation

False. A finite set with \(n\) elements cannot be put into bijection with any proper subset (which has at most \(n-1\) elements). This is not just obvious — it requires proof — but the result holds rigorously. The fact that infinite sets can match their proper subsets is precisely what distinguishes them from finite sets and makes the concept of infinity so counterintuitive.