this post was submitted on 27 Jun 2024
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Science Memes

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I just cited myself. (mander.xyz)
submitted 5 months ago by [email protected] to c/[email protected]
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[–] [email protected] 43 points 5 months ago (2 children)

0.9<overbar.> is literally equal to 1

[–] [email protected] 19 points 5 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
[–] [email protected] 8 points 5 months 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 5 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.

[–] [email protected] 1 points 5 months ago (1 children)

ELI5

[–] [email protected] 2 points 5 months ago

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

[–] [email protected] 3 points 5 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.

[–] [email protected] 2 points 5 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.

[–] [email protected] 2 points 5 months ago

That actually makes sense, thank you.

[–] [email protected] -4 points 5 months ago (1 children)

0.9 is most definitely not equal to 1

[–] [email protected] 9 points 5 months ago (1 children)

Hence the overbar. Lemmy should support LaTeX for real though

[–] [email protected] 7 points 5 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

[–] [email protected] 3 points 5 months ago

Oh lol its rendering as HTML for you.