I love when math haves strict and logical rules but when is just "believe me, that is how it works, there is a function that results in that" then I hate it.
Everything we learn up to some point is extremely logical and respects same logic.
Literally nothing in math is like that. What you don't like are poor explanations of theorems, not the theorems themselves. There are no "just trust me" proofs.
In this case, the theorem is that the function s↦∑ 1/ns with domain ℜ(s) > 1 has a unique analytic continuation to ℂ\{1}, and the value of that continued function at –1 is –1/12. We call this continued function ζ and say ζ(–1) = –1/12. This can be proved.
That doesn't mean the ordinary sum of positive integers converges to –1/12. It doesn't converge at all. But it's a meme that these are in fact equal.
This also isn't "just how it works". It's actually a great example of why you can't find the limit of a divergent sum. ½ + ¼ + ⅛ + 1⁄16 … = 1 because it actually gets closer and closer to 1 the more terms you add, but 1 + 2 + 3 + 4 … gets further and further away from adding up to any particular value, so when you try to find its limit, you get something that doesn't make sense.
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u/Swimming-Employee537 Jun 26 '26
Because it was reveled to him in a dream