— onion


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onion #5958

what are your favorite theorems? one of mine is "this is a theorem (of peano arithmetic)", it's expressible by the diagonal lemma and is a consequence of Löb's theorem. another is Kőnig's lemma, I think it's neat and it's especially interesting in reverse mathematics, where weaker forms of it lead to interesting systems.

onion (edited ) #5418

caesar, it is not nonsense to give the value -1/12 to the sum of all natural numbers. It is misleading to say that it equals -1/12 when the method used to get that result is not specified but when it is then it can be proven. It's really just a matter of definition : under the usual definition of infinite series it doesn't exist, but under Ramanujan summation it's -1/12. It turns out that some models used in physics (not just string theory) give the same value to that infinite sum as Ramanujan summation, but they do not need the sum to fundamentally be equal to -1/12 and they do not imply that even if they accurately describe the world (because that doesn't mean anything if we can't agree on definitions), they only imply that you can get that result if you use that particular definition of what the value of an infinite sum is

onion #2928

orange :)