• 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.

    • 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

    • 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.