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 7 months ago by [email protected] to c/[email protected]
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[–] [email protected] 75 points 7 months ago (48 children)

2/9 = 0.222... 7/9 = 0.777...

0.222... + 0.777... = 0.999... 2/9 + 7/9 = 1

0.999... = 1

No, it equals 1.

[–] [email protected] 24 points 7 months ago (1 children)

Similarly, 1/3 = 0.3333…
So 3 times 1/3 = 0.9999… but also 3/3 = 1

Another nice one:

Let x = 0.9999… (multiply both sides by 10)
10x = 9.99999… (substitute 0.9999… = x)
10x = 9 + x (subtract x from both sides)
9x = 9 (divide both sides by 9)
x = 1

[–] [email protected] 16 points 7 months ago (1 children)

My favorite thing about this argument is that not only are you right, but you can prove it with math.

[–] [email protected] 0 points 7 months ago (6 children)

you can prove it with math

Not a proof, just wrong. In the "(substitute 0.9999… = x)" step, it was only done to one side, not both (the left side would've become 9.99999), therefore wrong.

[–] [email protected] 0 points 7 months ago (1 children)

They multiplied both sides by 10.

0.9999... times 10 is 9.9999...

X times 10 is 10x.

[–] [email protected] 0 points 7 months ago

X times 10 is 10x

10x is 9.9999999....

As I said, they didn't substitute on both sides, only one, thus breaking the rules around rearranging algebra. Anything you do to one side you have to do to the other.

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[–] [email protected] 18 points 7 months ago (1 children)

That's the best explanation of this I've ever seen, thank you!

[–] [email protected] 8 points 7 months ago* (last edited 7 months ago) (1 children)

That's more convoluted than the 1/3, 2/3, 3/3 thing.

3/3 = 0.99999...

3/3 = 1

If somebody still wants to argue after that, don't bother.

[–] [email protected] 6 points 7 months ago* (last edited 7 months ago)

Nah that explanation is basically using an assumption to prove itself. You need to first prove that 1/3 does in fact equal .3333... which can be done using the 'convoluted' but not so convoluted proof

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