this post was submitted on 27 Jun 2024
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I just cited myself. (mander.xyz)
submitted 1 month ago by [email protected] to c/[email protected]
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[–] [email protected] 44 points 1 month ago (2 children)

0.9<overbar.> is literally equal to 1

[–] [email protected] 19 points 1 month 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
[–] [email protected] 8 points 1 month ago (1 children)

Even simpler: 1 = 3 * 1/3

1/3 =0.333333....

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

[–] [email protected] 2 points 1 month 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 1 points 1 month ago (1 children)

ELI5

[–] [email protected] 2 points 1 month ago

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

[–] [email protected] 3 points 1 month 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.

[–] [email protected] 2 points 1 month 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.

[–] [email protected] 2 points 1 month ago

That actually makes sense, thank you.

[–] [email protected] -4 points 1 month ago (1 children)

0.9 is most definitely not equal to 1

[–] [email protected] 9 points 1 month ago (1 children)

Hence the overbar. Lemmy should support LaTeX for real though

[–] [email protected] 7 points 1 month 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

[–] [email protected] 3 points 1 month ago

Oh lol its rendering as HTML for you.