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Mind=Blown (lemmy.fmhy.ml)
submitted 1 year ago by upsiderue@lemmy.fmhy.ml to c/memes@lemmy.ml
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[-] upsiderue@lemmy.fmhy.ml 0 points 1 year ago

If .99....9=1, then 0.999...8=0.999...9, 0.99...7=0.999...8, and so forth to where 0=1?

[-] Tchallenge@social.fossware.space 51 points 1 year ago* (last edited 1 year ago)

The tricky part is that there is no 0.999...9 because there is no last digit 9. It just keeps going forever.

If you are interested in the proof of why 0.999999999... = 1:

0.9999999... / 10 = 0.09999999... You can divide the number by 10 by adding a 0 to the first decimal place.

0.9999999... - 0.09999999... = 0.9 because the digit 9 in the second, third, fourth, ... decimal places cancel each other out.

Let's pretend there is a finite way to write 0.9999999..., but we do not know what it is yet. Let's call it x. According to the above calculations x - x/10 = 0.9 must be true. That means 0.9x = 0.9. dividing both sides by 0.9, the answer is x = 1.

The reason you can't abuse this to prove 0=1 as you suggested, is because this proof relies on an infinite number of 9 digits cancelling each other out. The number you mentioned is 0.9999...8. That could be a number with lots of lots of decimal places, but there has to be a last digit 8 eventually, so by definition it is not an infinite amount of 9 digits before. A number with infinite digits and then another digit in the end can not exist, because infinity does not end.

[-] upsiderue@lemmy.fmhy.ml 9 points 1 year ago

Wonderful explanation. It got the point across.

[-] ripjackie@lemmy.dbzer0.com 5 points 1 year ago

That is the best way to describe this problem I've ever heard, this is beautiful

[-] wumpoooo@lemmy.world 2 points 1 year ago

Maybe a stupid question, but can you even divide a number with infinite decimals?

I know you can find ratios of other infinitely repeating numbers by dividing them by 9,99,999, etc., divide those, and then write it as a decimal.

For example 0.17171717.../3

(17/99)/3 = 17/(99*3) = 17/297

but with 9 that would just be... one? 9/9=1

That in itself sounds like a basis for a proof but idk

[-] quicksand@lemmy.world 2 points 1 year ago

Yes that's essentially the proof I learned in high school. 9/9=1. I believe there's multiple ways to go about it.

[-] DrMango@lemmy.world 2 points 1 year ago

This is the kind of stuff I love to read about. Very cool

[-] DesolateMood@lemm.ee 9 points 1 year ago

0.999...8 does not equal 0.999...9 so no

[-] TeddE@lemmy.world 2 points 1 year ago

If the "…" means 'repeats without end' here, then saying "there's an 8 after" or "the final 9" is a contradiction as there is no such end to get to.

There are cases where "…" is a finite sequence, such as "1, 2, … 99, 100". But this is not one of them.

[-] DesolateMood@lemm.ee 3 points 1 year ago

I'm aware, I was trying to use the same notation that he was so it might be easier for him to understand

[-] somePotato@sh.itjust.works 6 points 1 year ago

Your way of thinking makes sense but you're interpreting it wrong.

If you can round up and say "0,9_ = 1" , then why can't you round down and repeat until "0 = 1"? The thing is, there's no rounding up, the 0,0...1 that you're adding is infinitely small (inexistent).

It looks a lot less unintuitive if you use fractions:

1/3 = 0.3_

0.3_ * 3 = 0.9_

0.9_ = 3/3 = 1

[-] kadu@lemmy.world 4 points 1 year ago

Huh... Where did you get "0.999... = 0.999...8" from? There's a huge difference here.

[-] upsiderue@lemmy.fmhy.ml -4 points 1 year ago* (last edited 1 year ago)

Read carefully. I wrote a finite number(0.999...9)

[-] Cortell@lemmy.world 5 points 1 year ago

Think carefully

What does 0.99…8 represent to you exactly

If it’s an infinite amount of 9s then it can’t end in an 8 because there’s an infinite amount of 9s by definition so it’s not a real number

[-] dlove67@feddit.nl 3 points 1 year ago

There is no .99...8.

The ... implies continuing to infinity, but even if it didn't, the "8" would be the end, so not an infinitely repeating decimal.

[-] icosahedron@ttrpg.network 2 points 1 year ago

No, because that would imply that infinity has an end. 0.999… = 1 because there are an infinite number of 9s. There isn’t a last 9, and therefore the decimal is equal to 1. Because there are an infinite number of 9s, you can’t put an 8 or 7 at the end, because there is literally no end. The principle of 0.999… = 1 cannot extend to the point point where 0 = 1 because that’s not infinity works.

[-] XpeeN@sopuli.xyz 2 points 1 year ago* (last edited 1 year ago)

If you really wants to understand the concept , you need to learn about limits

this post was submitted on 17 Jul 2023
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