This seems undeniably true to me, but I don't know how to write it down.
Given the non-empty set $S$ containing only natural numbers (starting at 1, not 0). If for every number $x$ greater than 1 there is a number $y$ such that $y<x$, then 1 must be in the set $S$.
I think this must be true, because you can start at any natural number, and take a smaller number, and a smaller number than that, smaller than that and so forth, until you arrive at 1. But how do you actually write this proof down?