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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You cannot do anything an infinite number of times The answer to "1+2+3+4+5+... = x" is that x can't be anything because you will never actually finish adding up numbers and you will never get an answer "Infinite" is another way of saying "nonexistent"
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You can't say x="infinity" or ∞ because in ordinary arithmetic that's not a number, it's a meaningless word
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Replying to @arthur_affect
I’d argue against meaningless. It’s very meaningful, but it’s not an actual attainable thing. If infinity is meaningless, imaginary numbers (sqrt(-1)) are meaningless since it cannot be found in nature.
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Replying to @KHMakerD
Oh, I'll backtrack quickly on this one -- "infinity" *as most people use it* doesn't have very *much* meaning because they don't define what they're talking about Cantor, who spent his life studying the concept of infinity, jumped very quickly past ∞ to infinities, plural
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Replying to @arthur_affect @KHMakerD
So, in other words, he went to infinity...and beyond?
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Replying to @beetlefella101 @KHMakerD
There's an infinite number of infinities He even went ahead and defined "absolute infinity" (Ω) and said that's the name for an infinity so big that none of the properties he'd just mathematically explored applied to it
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(Sort of supporting the point Spengler would later make about "infinity" being a peculiarly European Christian cultural concept, Cantor was a *very* devout Christian who saw his mathematics as a logical extension of the whole "Can God make a rock so big he can't lift it" stuff)
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He was kind of caught between worlds here, because the other mathematicians -- most of whom weren't particularly devout -- often thought of his work as a weird waste of time, while the Church didn't understand what he was talking about and thought it sounded like witchcraft
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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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Cantor thought a lot about why ∞ doesn't actually make sense and in order to work with the idea split it into pieces, defining a difference between cardinal and ordinal numbers It's a whole thing that, honestly, the more I think about it the less confident I am at explaining it
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**kicks in the door** SET THEORY BABY!
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Underrated0 replies 0 retweets 1 like
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Just wait until you get to ordering!
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