This is a fun one, because of course the kneejerk rejection of the statement "1+2+3+4+5+... = -1/12" is correct Under everyday, ordinary grade-school arithmetic, the answer can't be "-1/12" -- but the answer can't be any other number either, the operation itself is not possiblehttps://twitter.com/tomgabion/status/1289857027381002241 …
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Anyway, Cantor's idea of infinity (the "transfinite numbers") aren't really the same thing as what people mean when they put ∞ as the "sum" for a divergent series like 1+2+3+4+...
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A lot of people lose the thread on what ∞ is, or what a limit is. It’s a convention, a set of instructions. You can get as large/small/close as you need to for whatever practical task you’re using the numbers for. But ∞ doesn’t actually exist as a number.
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