this post was submitted on 27 Jun 2024
792 points (95.1% liked)

Science Memes

11148 readers
1835 users here now

Welcome to c/science_memes @ Mander.xyz!

A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.

Rules

  1. Don't throw mud. Behave like an intellectual and remember the human.
  2. Keep it rooted (on topic).
  3. No spam.
  4. Infographics welcome, get schooled.

This is a science community. We use the Dawkins definition of meme.

Research Committee

Other Mander Communities

Science and Research

Biology and Life Sciences

Physical Sciences

Humanities and Social Sciences

Practical and Applied Sciences

Memes

Miscellaneous

founded 2 years ago
MODERATORS
Sal@mander.xyz
fossilesque@mander.xyz
SciBot@mander.xyz
792
I just cited myself. (mander.xyz)
submitted 4 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
231 comments fedilink hide all child comments
 
you are viewing a single comment's thread
view the rest of the comments
[–] UnderpantsWeevil@lemmy.world 19 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.