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In response to "Technically false, but the technicality is so minuscule that it's irrelevant. -- nm" by TWuG

my favourite proof of this is

Posted by Reagen (aka Reagen) Mar 5 '10, 12:39

1/3 + 1/3 + 1/3 = 1
1/3 = .3333....
so .3333.... + .3333.... + .3333.... = .9999....

Responses:

and this is why Vulcans ultimately took a backseat to humans in the Federation -- nm - crash davis Mar 5, 12:44
That math seems hinky. Because, on its face, 1 /= .999.... - TWuG Mar 5, 12:44 51
- I think it's more to the idea that .333... does not actually equal 1/3. - JaxSean Mar 5, 12:51 40
  - except that it does. - Reagen Mar 5, 12:53 26
    - just becorse you can express something does not mean it does not excist - Danedukenuuk Mar 5, 13:03 2
      - again, .333 != .333... -- nm - Reagen Mar 5, 13:04 1
        
        calculating precisely with infinite numbers is one of the harder mathematical diciplines - Danedukenuuk Mar 5, 13:07
    - I'd just say that there are somethings that can't be perfectly expressed in the decimal system -- nm - crash davis Mar 5, 12:55 22
      - it's perfectly expressed. .333..... means you take the 3s out to infinity. - Reagen Mar 5, 12:57 21
        
        .333 does not equal 1/3. It does conceptually, but not precisely. - JaxSean Mar 5, 13:00 5
        
        maybe this is the problem: .333 != .333.... - Reagen Mar 5, 13:03 3
        
        I understand. I just neglected the ... - JaxSean Mar 5, 13:05 2
        
        but you can't and mean the same thing. -- nm - Reagen Mar 5, 13:09 1
        
        I think we'll all agree we're talking about "0.333...." in this string. -- nm - JaxSean Mar 5, 13:10
        
        [deleted]
        
        but thats not perfect, because you don't get 1 when you multiply it by 3 -- nm - crash davis Mar 5, 12:59 14
        
        Yes you do, because .999.... = 1 :) -- nm - oblique Mar 5, 13:00 13
        
        You can't argue that .9999... = 1 *because* .9999.... = 1. That's circular logic. - TWuG Mar 5, 13:03 8
        
        we're not arguing "it is because it is". There's a couple proofs been offered. - Reagen Mar 5, 13:05 7
        
        Yes. There. Is. It's just "infinitesimally small." -- nm - JaxSean Mar 5, 13:07 2
        
        but because infinity never stops, there is no difference. -- nm - Reagen Mar 5, 13:08 1
        
        there will always be a difference itss just getting idefinately smaller and smaller -- nm - Danedukenuuk Mar 5, 13:11
        
        part of the problem I have is that you say "when you go out to infinity" like its a place you can stop at -- nm - crash davis Mar 5, 13:06 3
        
        Yeah. Infinity can never be reached. That .9 keeps trying to be 1, but it'll never arrive. It's like Zeno's Paradox. - TWuG Mar 5, 13:10
        
        No, it's an acknowledgement that it *can't* stop. -- nm - mara Mar 5, 13:08 1
        
        and thus it can never be equal, because the difference can't be stopped at either -- nm - crash davis Mar 5, 13:09
        
        no, because there is always an infinitely small distance between them -- nm - crash davis Mar 5, 13:03
        
        that's only true if the universe stops expanding -- nm - Beryllium Mar 5, 13:01
        
        False. -- nm - JaxSean Mar 5, 13:01
        
        *pop* -- nm - brains Mar 5, 13:01
  - But it is the number you get when divide 1 by 3. -- nm - Inigo Mar 5, 12:52 9
    - that is an imprecise number, the accurate answer is 1/3 -- nm - crash davis Mar 5, 12:54 8
      - It's not though. .infinite3s is what you get when divide 1 by 3. -- nm - Inigo Mar 5, 12:56 5
        
        just admit you cannot use the decimal system perfectly when you divide 1 by 3 -- nm - crash davis Mar 5, 13:01 2
        
        Just admit Edgar's defensive kung fu was weak. -- nm - Inigo Mar 5, 13:03
        
        sure you can. That's what the ... is for. -- nm - Reagen Mar 5, 13:03
        
        .ketchupketchupketchup..... -- nm - Reagen Mar 5, 12:57 1
        
        Heh. He'd like the idea of .ketchup (bar). -- nm - Inigo Mar 5, 13:00
      - not when you take it out to infinity. -- nm - Reagen Mar 5, 12:55 1
        
        and then I'll just Buzz Lightyear it -- nm - crash davis Mar 5, 12:58
  - No goatee today! -- nm - crash davis Mar 5, 12:52 2
    - Because I'm on your side! -- nm - JaxSean Mar 5, 12:52 1
      - If it walks like a trap and talks like a trap... -- nm - Spawn Mar 5, 12:54
- it's not that it's too small to measure, it's that there is no difference. - Reagen Mar 5, 12:49 8
  - Converting a fraction to a decimal introduces error. 1/3 is an exact number, but less precise than .333... - TWuG Mar 5, 12:52 4
    - .33 is an approximation. .33.... is an exact number. -- nm - Reagen Mar 5, 12:53 3
      - No it isn't. It's a conceptual number, because it's never ending, and we could never write it. -- nm - JaxSean Mar 5, 13:02 2
        
        that's what ... is for, to save us time. -- nm - Reagen Mar 5, 13:06 1
        
        In other words, we round the number to make it easier. - JaxSean Mar 5, 13:09
  - Because: see above. -- nm - JaxSean Mar 5, 12:51
  - This is why we haven't converted to your silly metric system. -- nm - Max Mar 5, 12:51 1
    - No, it's just because you have to be different -- nm - Roger More Mar 5, 12:52
- I think its a failure of mathematical equations to captured something that can be perfectly expressed in a few short words -- nm - crash davis Mar 5, 12:46

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my favourite proof of this is

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