Welcome, mathletes! Today, we're going to explore the Paradox of the Infinite Sock Drawer.
Imagine a sock drawer with infinitely many socks, each pair perfectly matched. But, as we reach in and grab a sock, the drawer paradoxically refills itself. How do we know the drawer isn't actually empty?
Consider the following theorem: The Sock Drawer is Not a Sock Drawer at All. This proof is based on the fundamental principle of Socky McSockface's Sock Drawer Paradox.
Let S be the set of all socks in the drawer. If we define not S to be the set of all non-socks, then clearly, S is a proper subset of not S.
But wait, if S is a proper subset of not S, then it must be the case that S is empty, since not S is the complement of S and the complement of a nonempty set is never empty.
However, we know that S is not empty, since we can see the socks in the drawer. Thus, we have a contradiction, and we conclude that S is actually not a Sock Drawer at All.