• funnystuff97@lemmy.world
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      1 year ago

      A very wrong proof once showed that the sum of all positive integers (1 + 2 + 3 + 4…) was -1/12. In reality, the infinite sum has no solution, so this proof became something of a meme.

        • BossDj@lemm.ee
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          1 year ago

          One of those cases where “first you learn the rules. Then you can learn how to break them.”

      • soloner@lemmy.world
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        1 year ago

        Fr I didn’t know what I was doing and tried it … broke both of my legs and gave me a concussion.

        Don’t mess around with -1/12!

      • Tavarin@lemmy.ca
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        1 year ago

        I don’t like the Ramanujan explanation at all because c - 4c doesn’t equal the divergent series, since 4c is only supposed to subtract from every other number, so it has more terms at every single limit of n, and thus more terms at infinity. So c - 4c is just -3c, not a divergent series.

          • Tavarin@lemmy.ca
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            1 year ago

            Except it is. Infinities can have different sizes, and the size of an infinity needs to be taken into account when working with them.

            Rama subtracted one infinity that is twice the size of another from it, so he subtracted twice as many numbers as his equation implies.

            • jana@leminal.space
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              1 year ago

              Infinities do have different sizes, yes. But not on that scale. Both of these are countably infinite sets.

              Think about this: there are infinitely many primes. Obviously, not every number is prime. But you can still map primes 1:1 with the natural numbers. They’re both the same size of infinity.

              • Tavarin@lemmy.ca
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                1 year ago

                Not when you’re adding them together.

                c - 4c = -3 - 6 - 9 - 12…

                In order to make c the same as the divergent series you have to subtract the series:

                f = 0 + 4 + 0 + 8 …

                Which is not the same series as 4c.

                  • Tavarin@lemmy.ca
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                    1 year ago

                    It makes the series equal length. You’ll notice this is discussed in the wikipedia article, and a bunch of bullshit handwaving has to be done to try and correct for it.

                    c - 4c = -3 - 6 - 9 - 12…

                    Simple as that, not some crap divergent series. Rama was a troll.

    • GCostanzaStepOnMe@feddit.de
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      1 year ago

      Basically there’s this meme that 1+2+3…= -1/12, which isn’t true, but is related to something that is true.

    • Shakizi@lemm.ee
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      1 year ago

      I’m not smart enough to explain it but it’s a reference to Ramanujan Summation if you want to read about it yourself.