this post was submitted on 27 Jun 2024
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Science Memes

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submitted 4 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
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[–] LodeMike@lemmy.today 44 points 4 months ago (2 children)

0.9<overbar.> is literally equal to 1

[–] UnderpantsWeevil@lemmy.world 18 points 4 months ago (3 children)

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
[–] LodeMike@lemmy.today 8 points 4 months ago (1 children)

Even simpler: 1 = 3 * 1/3

1/3 =0.333333....

1/3 + 1/3 + 1/3 = 0.99999999... = 1

[–] UnderpantsWeevil@lemmy.world 2 points 4 months ago (1 children)

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.

[–] SuperSaiyanSwag@lemmy.zip 1 points 4 months ago (1 children)

ELI5

[–] UnderpantsWeevil@lemmy.world 2 points 4 months ago

Mostly boils down to the pedantry of explaining why 1/3 = 0.(3) and what 0.(3) actually means.

[–] Swedneck@discuss.tchncs.de 3 points 4 months ago (1 children)

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.

[–] UnderpantsWeevil@lemmy.world 2 points 4 months 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.

[–] beejboytyson@lemmy.world 2 points 4 months ago

That actually makes sense, thank you.

[–] jonsnothere@beehaw.org -4 points 4 months ago (1 children)

0.9 is most definitely not equal to 1

[–] mathemachristian@lemm.ee 9 points 4 months ago (1 children)

Hence the overbar. Lemmy should support LaTeX for real though

[–] jonsnothere@beehaw.org 7 points 4 months ago (1 children)

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

[–] LodeMike@lemmy.today 3 points 4 months ago

Oh lol its rendering as HTML for you.