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I just cited myself. (mander.xyz)

submitted 4 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

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[-] UnderpantsWeevil@lemmy.world 19 points 3 months 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

[-] LodeMike@lemmy.today 8 points 3 months ago

Even simpler: 1 = 3 * 1/3

1/3 =0.333333....

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

[-] UnderpantsWeevil@lemmy.world 2 points 3 months 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.

[-] SuperSaiyanSwag@lemmy.zip 1 points 3 months ago

ELI5

[-] UnderpantsWeevil@lemmy.world 2 points 3 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 3 months 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.

[-] UnderpantsWeevil@lemmy.world 2 points 3 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.