Does 1+2+3+... Really Equal -1/12?
Tl;dr: No it doesn't. Under some unintuitive definition for infinite summation that is useful in some physical calculations it does which is surprising.<p>Under the normal rules which hold for direct use obviously the answer is positive infinity just like you would be expect, you're not stupid and you could be a mathematician if you wanted to.<p>edit: For fun, a short story:<p>If Muhammed is on top of a strangely shaped mountain that with every step down gets one step wider. The mountain is so high he can't see the bottom yet Muhammed wants to move this mountain. So Muhammed starts fetching horses and ties them to the mountain with ropes to move it. That's a direct use of this equality, and you can't stand from afar and look at the scene and say "my, I think that's about -1/12 horses Muhammed is fetching". You'll see Muhammed taking an infinite amount of time fetching an infinite number of horses, and you'll definitely seem him do it more than once.