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0.999999999.... = 1? watch

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    (Original post by philosophy_kid)
    bringing a philosophers mind to this.....

    1 = 1 a tautology

    so 1/3 cannot be 3.3333.... because 3.3333...x 3 = 9.99999 not 1.

    what this asks is: is 1/3 possible? does 'a third' exist... absolutely that is.
    another possibility is that 1 is simply for symbol for something which isn't actually 1?

    Conjecture, yes. But more useful than simply accepting the inadequacy of the mathematical answer.
    Well, work in base three rather than base ten and you'll see that a third is 0.1, and three times that is 10 * 0.1 = 1. So yes, a third exists...
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    It converges upon one such that it is one.
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    (Original post by RestrictedAccess)
    yeh that was drilled into us from year 9 for all of about a lesson, the other proof is:

    if x = 0.99999....
    10x = 9.99999.....
    10x -x = 9
    9x = 9
    x = 9/9
    x=1

    so 0.99... = 1
    No that only works because by placing ... you mean to say 0.999 to infinity= 1, thats like saying:

    if x=1
    10x=10
    10x-x=9
    x=9/9
    x=1

    I'm probably confusing you and being overly picky about it, but I thought I'd just point it out.
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    Yeah I think the infinite series method on wiki is best, for something like this you want to keep it in fractions.
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    (Original post by Spire)
    No that only works because by placing ... you mean to say 0.999 to infinity= 1, thats like saying:

    if x=1
    10x=10
    10x-x=9
    x=9/9
    x=1

    I'm probably confusing you and being overly picky about it, but I thought I'd just point it out.
    Don't see what you're trying to do. But you're a Selwynite, so I'll let you off.
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    I don't believe it.

    Humans just can't interpret the number 0.99 repeating as it is infinitely long. It gets closer and closer but never does reach it.
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    The only reason that this is confusing is because of the restrictions of our number system. If our numbers went up a zero every 6, then we wouldn't have this problem. But 10/3 is an impossible sum, unless you keep it as a surd.

    0.999 recurring isn't a real number. What do you add to it to make it 1? O yea lol, you can't because there's no space between the two numbers to add anything. It's infinite.
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    (Original post by fieryiceissweet)
    umm yes
    for goodness sake i know that and im only 16
    dont be surprised if you get a lot of negs for a dumb question which you could have googled
    Shut uuuuup.
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    further proof that gcse's don't= intelligence.
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    I know of a similar one to yours where:

    1/9 = 0.1111111..........
    1/9 * 9 = 1 AND 0.1111111...... * 9 = 0.9999999
    therefore 0.99999..... == 1
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    (Original post by generalebriety)
    Well, work in base three rather than base ten and you'll see that a third is 0.1, and three times that is 10 * 0.1 = 1. So yes, a third exists...
    How can a third = 0.1?
    I'm no mathematician, but it seems like the same case as Xeno's paradox.
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    (Original post by purplefrog)
    I know of a similar one to yours where:

    1/9 = 0.1111111..........
    1/9 * 9 = 1 AND 0.1111111...... * 9 = 0.9999999
    therefore 0.99999..... == 1

    so if 1/9 and 0.1 are the same... shouldn't they multiply to make the same thing?
    0.999999... and 1 not being the same and all?
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    (Original post by generalebriety)
    Don't see what you're trying to do. But you're a Selwynite, so I'll let you off.
    Hehe Well it just doesn't seem right to me, by saying x=0.999... you might as well say x=1 and by saying 10x=9.999... you might as well say 10x=10 and then carry out the same method (to get x=1), the proof just follows that logic- but it's just one of those things that's really hard to explain to someone else. I prefer the infinite series method.
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    (Original post by PeterR)
    I don't believe it.

    Humans just can't interpret the number 0.99 repeating as it is infinitely long. It gets closer and closer but never does reach it.
    Err, 0.99... is perfectly well defined, and it is equivalent to 1. There is a branch of mathematics which has made the formulation perfectly rigourous; it derives these results from first principles, so that we can be sure our work rests on stable foundations.
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    And mathematicians like to pretend they have all the answers...
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    (Original post by philosophy_kid)
    How can a third = 0.1?
    In base 3...

    I'm no mathematician, but it seems like the same case as Xeno's paradox.
    Yes, and Zeno's paradox is not a paradox, in the same way that 0.99.. = 1.
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    (Original post by Kolya)
    In base 3...

    Yes, and Zeno's paradox is not a paradox, in the same way that 0.99.. = 1.
    I'm not sure if you're aware or not but I do remember mentioning that I am no mathematician so "base 3" could mean "mathematicians are all arrogant tw*ats" as far as i'm concerned.
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    If you consider the text 0.9 you are 0.1 away from being equal to 1. For each digit after you successively set it to the digit that makes the value closest to 1. So it appears to converge to 1; in fact each "iteration" the difference between 1 and 0.9... becomes 10 times less. So if the modulus error, p \propto 10^{-n} then all you must prove is that as n tends to infinity, p equals 0.

    p = k*10^{-n}
    0.1 = k*10^{-1} implies k = 1
    p = 10^{-n}

    Now the question is more philosophical: does p ever reach zero even with an infinite n?
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    This has gotten an awful lot more complicated than I'd thought!
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    (Original post by philosophy_kid)
    How can a third = 0.1?
    Each "column" in decimal represent another power of ten:

    ... 10^{3}, 10^{2}, 10^{1}, 10^{0}, 10^{-1}, 10^{-2}, 10^{-3} ...

    If you want to make a third you have to make it up out of the columns. But for base three the columns are:

    ... 3^{3}, 3^{2}, 3^{1}, 3^{0}, 3^{-1}, 3^{-2}, 3^{-3} ...

    So 1/3 = is ...+0*9+0*3+0/1+1/3+0/9+0/27+...
 
 
 
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