Comment on I just cited myself.

LodeMike@lemmy.today ⁨2⁩ ⁨years⁩ ago

• UnderpantsWeevil@lemmy.world ⁨2⁩ ⁨years⁩ ago

  There’s a Real Analysis proof for it and everything.

  Basically boils down to

  • If 0.(9) != 1 then there must be some value between 0.(9) and 1.
  • We know such a number cannot exist, because for any given discrete value (say 0.999…9) there is a number (0.999…99) that is between that discrete value and 0.(9)
  • Therefore, no value exists between 0.(9) and 1.
  • So 0.(9) = 1

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  • LodeMike@lemmy.today ⁨2⁩ ⁨years⁩ ago

    Even simpler: 1 = 3 * 1/3

    1/3 =0.333333…

    1/3 + 1/3 + 1/3 = 0.99999999… = 1

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    • UnderpantsWeevil@lemmy.world ⁨2⁩ ⁨years⁩ ago

      Even simpler

      0.99999999… = 1

      But you’re just restating the premise here. You haven’t proven the two are equal.

      1/3 =0.333333…

      This step

      1/3 + 1/3 + 1/3 = 0.99999999…

      And this step

      Aren’t well-defined. You’re relying on division short-hand rather than a real proof.

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      • SuperSaiyanSwag@lemmy.zip ⁨2⁩ ⁨years⁩ ago

        ELI5

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  • Swedneck@discuss.tchncs.de ⁨2⁩ ⁨years⁩ ago

    the explanation (not proof tbf) that actually satisfies my brain is that we’re dealing with infinite repeating digits here, which is what allows something that on the surface doesn’t make sense to actually be true.

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    • UnderpantsWeevil@lemmy.world ⁨2⁩ ⁨years⁩ ago

      Infinite repeating digits produce what is understood as a Limit. And Limits are fundamental to proof-based mathematics, when your goal is to demonstrate an infinite sum or series has a finite total.

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  • beejboytyson@lemmy.world ⁨2⁩ ⁨years⁩ ago

    That actually makes sense, thank you.

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• jonsnothere@beehaw.org ⁨2⁩ ⁨years⁩ ago

  0.9 is most definitely not equal to 1

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  • mathemachristian@lemm.ee ⁨2⁩ ⁨years⁩ ago

    Hence the overbar. Lemmy should support LaTeX for real though

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    • jonsnothere@beehaw.org ⁨2⁩ ⁨years⁩ ago

      Oh, that’s not even showing as a missing character, to me it just looks like 0.9

      At least we agree 0.99… = 1

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      • LodeMike@lemmy.today ⁨2⁩ ⁨years⁩ ago

        Oh lol its rendering as HTML for you.

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