• ledtasso@lemmy.world
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        1 year ago

        This one has always bothered me a bit because …999999 is the same as infinity, so when you’re “proving” this, you’re doing math using infinity as a real number which we all know it’s not.

        • yetAnotherUser@feddit.de
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          1 year ago

          Yes, you’re right this doesn’t work for real numbers.

          It does however work for 10-adic numbers which are not real numbers. They’re part of a different number system where this is allowed.

        • Snazz@lemmy.world
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          1 year ago

          You can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series.

          Sum(ar^n, n=0, inf) = a/(1-r)

          So,

          …999999

          = 9 + 90 + 900 + 9000…

          = 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3…

          = Sum(9x10^n, n=0, inf)

          = 9/(1-10)

          = -1