P-adics Memes

So you're innocently learning about p-adic numbers (those weird alternate number systems mathematicians invented because regular numbers weren't confusing enough), and you decide to check what ...11111₁₃ equals in base 13. Seems harmless, right? Wrong. It equals -1/12. You know, that same cursed result that shows up when you naively sum all positive integers (1+2+3+4+...) using analytic continuation. The mathematical equivalent of finding the same Easter egg in two completely different video games. Your brain does the uncomfortable double-take because somehow, in the twisted logic of p-adics, an infinite string of ones doesn't blow up to infinity—it just casually sits there being negative and fractional. Mathematics really said "let's make infinity mean something completely different" and called it a day.