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  1. #421
    Registered User Absane's Avatar
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    Anyway gTownTrey.... you are likely correct in what you are talking about, but I think you are choosing your words incorrectly. I say thi because at first, everything you were saying just wasn't making sense to me. When you quoted you calc book, I could see exactly what you are talking about. So, I'll rep you for truce.
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  2. #422
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    Originally Posted by Lance Uppercut View Post
    There does have to be a C. You would agree that there is a number between 10 and 20, right? And then you would agree that there is a number between 10 and 11, right? What about .999... and 1?
    if you so vehemently believe that there must be a number between 0.999... and 1 then you can see that there is indeed a difference
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  3. #423
    mad scientist gTownTrey's Avatar
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    Originally Posted by Absane View Post
    I don't think I ever actually tried to prove 0.999... = 1 since there are dozens of proofs in existence. My whole point was to defend and clarify everything we use to state that 0.999... = 1.

    But in the example given by your book, the author was talking about our ability to do a physical summation over an infinite number of terms. I agree we can never find a number this way. In pure mathematics, we don't concern ourselves with what is possible to do in the real world.

    However, we can prove that the summation sequence does have a least upper bound. My whole point in some argument back there was that 0.999... represents this least upper bound of the summation series, or just the set (0, 0.9, 0.99, ...). Once we agree that this number is the least upper bound, we can proceed to show that 0.999... = 1 by proving no number exists between the two (proof by contradiction).
    I agree. What I disagree with are the fact that the "proofs" of .999... = 1 aren't pure mathematical proofs, they are more like conjectures with a little rounding here and there. Proving that there is a least upper bound to .999... when compared with 1 does not prove that it is 1, it just shows it is the closest thing to 1. I'm going to use whole numbers in a rebuttle to show that in [0,5) there exists a least upper bound "n" , namely n = 4 between [0,5). However just because 4 is the least upper bound to 5, it isn't 5. It never will be 5 just as .999... will never be 1. If it did reach 1 then you could use the same least upper bound argument to show that you can reach a whole in a plane. If you notice on wikipedia, in almost all the "proofs" they use "1/3 = .333..." or something similar when in fact .333... != 1/3, it is simply the decimal reprisentation of 1/3 just as the convergent summation s(n) = 2 does not equal 2, it is just the representation of convergence.
    Last edited by gTownTrey; 05-21-2007 at 01:03 AM.
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  4. #424
    mad scientist gTownTrey's Avatar
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    Originally Posted by Absane View Post
    Anyway gTownTrey.... you are likely correct in what you are talking about, but I think you are choosing your words incorrectly. I say thi because at first, everything you were saying just wasn't making sense to me. When you quoted you calc book, I could see exactly what you are talking about. So, I'll rep you for truce.
    I will def. rep you back because I rarely hear intelligent people talk on these boards and I enjoyed having this discussion with you. It's always nice to have good discussions. I agree in truce. I am never one with words and I'm sure I used incorrect ones all over the place. I have a hard time writing what I'm thinking and it's a real problems when I'm trying to write abstracts and stuff hahaha. Sorry about all the confusion.
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  5. #425
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    Originally Posted by OmniPotentTitan View Post
    one number follows another number, is that hard to comprehend ?
    Well, given two numbers a and b that are real numbers that are not equal, yes, we can say that a > b or b > a. However, you make the assumption, whether you know it or not, that all the real numbers can be listed in some way. As the the mathematician Cantor has shown, one cannot do it. Here you can find a proof: http://www.classy.dk/log/archive/000906.html
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  6. #426
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    Originally Posted by gTownTrey View Post
    I'm going to bed after this point and a few rebuttles to thomas and finney that people have, but I know people are quoting convergent series definitions and such so before I went to bed I figured I would open up one of the calculus textbooks I have sitting here. The textbook: Addison-Wesley Elements of Calculus and Analytic Geometry, by Thomas and Finney. In this version it is on page 646 and it defines and explanes a convergent series: I quote


    "Can we actually add an infinite number of terms? The answer we give is the one usually given: Start at the beginning and add a finite number of terms, in order, one at a time (Fig. 11.7). This process yields a related sequence of numbers {s(n)}. [it shows a basic sequence here] Which appears to converge to the limit 2. We can show that [through a simple calculation] lim s(n) = 2. In this sense we say that the sum of the series s(n) is 2. Is the sum of any number of terms in this series 2? NO. Can we actually add an infinite number of yerms? NO. It is only in the sense that the sequence of partial sums s(n) converges to the limit 2 that we say "the sum of the series is 2."


    There, to whomever said that .999... = 1 because of any proof stating converging series actually yield a sum is incorrect. They do not yield any sums, because the number converges to 1. It does not = 1. The statement ".999... = 1" shows that .999... converges to 1 it is simply written .999...=1. That clear enough? I quoted the exact textbook explanation. the only thing I added was "NO". It was actually written "No."
    From your own quote:
    "It is only in the sense that the sequence of partial sums s(n) converges to the limit 2 that we say 'the sum of the series is 2'."

    Obviously, we can't add up an infinite number of terms because they are infinite.

    Let me take it a little further:

    0.999... = 0.9 + 0.09 + 0.009 + ...
    0.999... = 9*10^-1 + 9*10^-2 + 9*10^-3 + ...
    0.999... = sum(9*10^-n) where n=1 and n -> infinity
    0.999... = limit[sum(9*10^-n) where n=1 and n -> N], N -> infinity
    0.999... = limit[9*10^-1 + 9*10^-2 + ... + 9*10^-N], N -> infinity
    0.999... = limit[0.9 + 0.09 + 0.009...], N -> infinity
    0.999... = limit[0.999...], N -> infinity
    0.999... = limit[1 - 10^-N], N -> infinity
    0.999... = (limit[1], N -> infinity) - (limit[10^-N], N -> infinity)
    0.999... = 1 - 0
    0.999... = 1
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  7. #427
    RedRedRedRedRed Joemama06's Avatar
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    The way I see it.. the seemingly nonexistant difference in time would eventually become noticable if you did this with a million computers. the very small lengths of time would eventually add up to the point where the first computer would have booted up already while say the millionth would not be done booting at the same time. and if there were an infinite number of computers that this occurred with the difference in booting times would just get larger and larger.

    it reminds me of the idea they had in office space to steal money from the company by taking fractions of cents of transactions and putting it into an account. it wouldnt be much at first but over time that would add up to alot of money.
    Last edited by Joemama06; 05-21-2007 at 01:09 AM.
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  8. #428
    Hypotheses Non Fingo Errorist's Avatar
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    http://www.tenthdimension.com/flash2.php
    That have anything to do with what you guys are talking about?
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  9. #429
    mad scientist gTownTrey's Avatar
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    Originally Posted by yoda05378 View Post
    From your own quote:
    "It is only in the sense that the sequence of partial sums s(n) converges to the limit 2 that we say 'the sum of the series is 2'."

    Obviously, we can't add up an infinite number of terms because they are infinite.

    Let me take it a little further:

    0.999... = 0.9 + 0.09 + 0.009 + ...
    0.999... = 9*10^-1 + 9*10^-2 + 9*10^-3 + ...
    0.999... = sum(9*10^-n) where n=1 and n -> infinity
    0.999... = limit[sum(9*10^-n) where n=1 and n -> N], N -> infinity
    0.999... = limit[9*10^-1 + 9*10^-2 + ... + 9*10^-N], N -> infinity
    0.999... = limit[0.9 + 0.09 + 0.009...], N -> infinity
    0.999... = limit[0.999...], N -> infinity
    0.999... = limit[1 - 10^-N], N -> infinity
    0.999... = (limit[1], N -> infinity) - (limit[10^-N], N -> infinity)
    0.999... = 1 - 0
    0.999... = 1
    From my own quote, it says "partial sums s(n) converges to the limit". Any sum you take converges to the limit. Converges is the key word here. They converge. They don't equal. You say equal because equal is the representation of convergence. It is not the same equal as in 1+1=2. 1+1 actually equals 2. 1+1 does not converge to 2, it equals it.

    I honestly don't see the point in arguing with a calculus textbook on whether or not series actually yield a sum. They yield a number that converges to a sum. No matter what way you look at it that "=" sign everywhere you have typed is just a calculus representation of convergence when dealing with series. If you replaced the "=" with it's true definition here, convergence, the end of your argument would state:

    0.999... converges to (limit[1], N -> infinity) - (limit[10^-N], N -> infinity)
    (limit[1], N -> infinity) converges to 1
    (limit[10^-N], N -> infinity) converges to 0
    Therefore, .999... converges to 1-0
    .999... converges to 1.

    I literally took that right out of the textbook. Anyone can feel free to look up convergence in any textbook, and I can assure you (if it's a real textbook, not "Calculus 101 by Bb.com misc") that convergence approaches a number and does not reach it.
    Last edited by gTownTrey; 05-21-2007 at 01:18 AM.
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  10. #430
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    Originally Posted by Absane View Post
    You never responded to me when I quoted what you said a while back.
    you have done that multiple times to valid posts , you just cant refute good arguments so you go after the ones you cant understand and try to twist them around
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  11. #431
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    Originally Posted by Absane View Post
    You to seem to have a problem with logic. Does the limit of that sequence say anything the equality or inequality of 0.999... and 1? No. Nothing. I was explaining how 0.999... is not the same thing is the sequence (0, 0.9, 0.99, ...). I had explain the difference between the two because too many people kept saying that 0.999... is infinite.




    Now that I discredited your above claim, explain how the real numbers have gaps in them.
    i never claimed anything about gaps

    you keep asking me to find a c and i keep telling you there need not be one for 0.9999999999999999 to be less than 1

    i mean just look at the damn numbers.
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  12. #432
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    Originally Posted by Absane View Post
    Yes, 0.499... = 0.5.



    I can't provide a number because I know that one does not exist. I'm asking you to provide one because you claim one does exist.
    so whats the number lower than 0.999... ?



    0.888.. = 0.888.. just like 0.999... = 0.999... The former statement makes no claim that it is equal to another decimal representation.
    ah if 0.999... = 0.999... then it does not equal 1
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  13. #433
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    Originally Posted by Absane View Post
    I'm done with you. The fact that you said "there is an infinite c" after I repeatedly corrected your terminology is enough for me to give up on you.
    ah so when i prove you wrong you shall bail out, go for it.

    i love when someone tries to be all high and mighty when they cant even prove their assumptions, ive proved my facts once and over in every way you kept asking and you still cant understand.

    I didnt say "there is an infinite c", see this is where you begin crumbling under your weak argument and twisting my words again
    I said "unless you claim that there is an infinite c between 0.999... and 1 "

    so read the entire post intead of pulling things out of context




    i love it when people think they are automatically right and they "give up" as in they think they are still 100% right

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  14. #434
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    Originally Posted by Lance Uppercut View Post
    I have been mulling this over in my head for quite some time now, and I have nothing better to do this afternoon, so I thought I'd share my thought experiment disproving the existence of time with you all, today.

    A month or so ago, I posted a thread about .999... equaling 1, which stems from an idea from calculus called convergence. And since I use convergence to help me disprove time's existence, I'll go over it again in case some of you missed it.

    Basically, calculus states that whenever a number becomes infinitely close to another number that those two numbers are the same (i.e. .999... = 1). Here's a common example:

    1/3 = .333...
    .333... * 3 = .999...
    1/3 * 3 = 1

    It can be clearly seen that .333 * 3 = 1/3 * 3 and therefore that .999... = 1.

    If you can accept this as true, then hopefully you'll be able to understand how I have concluded that time does not exist.

    In my thought experiment, there are two computers; Computer A and Computer B. Computer A and B are the EXACT same in every possible way. They're 100% identical. Now, my question is, if upon turning on Computer A you then ISTANTANEOUSLY turn on Computer B, which computer will finish booting up first?

    The logical answer appears to be Computer A, since it was seemingly turned on "first." However, when taking convergence into account, that is not correct. They will boot up at the exact same time. According to my experiment, "after" turning on Computer A, Computer B is then INSTANTANEOUSLY turned on, which means that the time difference between the turning on of both computers, which is INFINITELY small, converges at zero, and they will therefore boot at the same time.

    Now, imagine you have one-million of these identical computers. If you turn on Computer A, then INSTANTANEOUSLY turn on Computer B, then INSTANTANEOUSLY turn on Comptuer C, until you turn on the one-millionth computer, what will be the time difference in booting between Computer A and the one-millionth computer? The answer? Zero. All one-million computers will boot at the exact same time. Refering back to the first example, the time difference between Computer A and Computer B was zero, which would mean that, since we're following the same rules, the time difference between Computer B and C is zero, which therefore means that the time difference between Computer A and Computer C is also zero. Following this, it can be seen that the time difference between Computer A and the one-millionth computer will continue to be zero.

    Taking this one step further now, what if there were an INFINITE number of these identical computers? You turn on Computer A and then INSTANTANEOUSLY turn on Computer B, and then C and then D and so on, for forever? When would Computer A finish booting? Never. None of the computers would EVER finish booting. As was just shown in the previous example, Computer A cannot finish booting until the very last computer boots, and since, in this example, there are an infinite number of computers, there is no end, and Computer A will simply be frozen, along with every proceeding computer for forever. Time remains at ZERO for eternity.

    That is why I don't believe in time's existence.

    What do you guys think?
    .999999... to an infinite number of 9's DOES NOT EQUAL 1. It gets infinitely close to 1, but it NEVER reaches 1.

    I'm going to find a math forum somewhere and post a link to this thread so that people can laugh at you.

    May God have mercy on your soul.
    Last edited by thirsty4chicken; 05-21-2007 at 01:53 AM.
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    Originally Posted by yanksbgood View Post
    Correct. But .999... gets so microscopically close to 1 that the difference between the two would be almost uncomputable by even the best calculators and thus the difference is almost negligent and .999... is for all intensive purposes rounded to 1. However .999... is a number that assumes the 9's repeat for ever. Thus, there is no number less than 1 but greater than .999... between .999... and 1.
    but there is still a difference

    that it is so small that its useless to not say that 0.999...=1 for practical purposes does not make it literally true
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    Originally Posted by yanksbgood View Post
    SOLUTION

    .999... can be rounded to 1 and is infinitely close, but is not 1. The problem in his argument lies in the fact that 1/3 is a definite portion of the whole (3/3), and cannot simply be converted to .333 repeating because 3 times that doesnt equal 1. It is instead ROUNDED to .333 repeating for simplicity, otherwise we would be forced to use fractions, because our number system is base 10, and 3 does not evenly go into 10.
    ^
    ^
    ^
    summary of everything i have said
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    Originally Posted by Absane View Post
    You are asserting I am wrong. Then, you explain your assertions by faulty intuitive arguments. I have provided formal mathematic arguments and you try your best to slip past them. Trust me, you are not the only one that has a problem with 0.999... = 1.

    If you are truly confident in your claims, why don't you go here (http://en.wikipedia.org/wiki/0.999.....m_in_education) and add your contribution?
    editing wikipedia is like talking to you
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    Originally Posted by gTownTrey View Post
    From my own quote, it says "partial sums s(n) converges to the limit". Any sum you take converges to the limit. Converges is the key word here. They converge. They don't equal. You say equal because equal is the representation of convergence. It is not the same equal as in 1+1=2. 1+1 actually equals 2. 1+1 does not converge to 2, it equals it.

    I honestly don't see the point in arguing with a calculus textbook on whether or not series actually yield a sum. They yield a number that converges to a sum. No matter what way you look at it that "=" sign everywhere you have typed is just a calculus representation of convergence when dealing with series. If you replaced the "=" with it's true definition here, convergence, the end of your argument would state:

    0.999... converges to (limit[1], N -> infinity) - (limit[10^-N], N -> infinity)
    (limit[1], N -> infinity) converges to 1
    (limit[10^-N], N -> infinity) converges to 0
    Therefore, .999... converges to 1-0
    .999... converges to 1.

    I literally took that right out of the textbook. Anyone can feel free to look up convergence in any textbook, and I can assure you (if it's a real textbook, not "Calculus 101 by Bb.com misc") that convergence approaches a number and does not reach it.
    The quote that you gave doesn't tell the whole story. Even I misunderstood and foolishly re-quoted your quote (I apologize, I've been studying all day for finals tomorrow and my brain is almost dead) when I should have seen the root of the misunderstanding and point out the fallacy of you providing that quote (I am not saying that the quote is wrong, merely that you are using the wrong one). I have also been careless in using "convergence" so that is my bad.

    Let me start over again. I am talking about the sum of the WHOLE geometric series. Not some, not partial. Consider a simple series: 1/2 + 1/4 + 1/8 + ...
    As more and more terms are added, we get closer and closer to 1. I believe that is what you're trying to show me and I agree with that.

    So we have established that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 is close to 1 and if we add 1/64 to the above we are even closer to 1, etc.

    Now this is my point: I am NOT trying to get "closer and closer" to 1. Instead, I am trying to get the ENTIRE sum of the infinite series. 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. If you have one blueberry pie and cut it in half, then cut each half another half, etc...you do NOT have the pie "converging" to one, do you? You still have one blueberry pie.

    If we are talking about partial sums, then we can describe the series of partial sums as "converging." But if we are talking about taking the ENTIRE infinite series, much like gluing back the blueberry pie slices into a whole pie, we are using the symbol "=", not the term "converging."

    1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1

    Not "converging to 1." But EQUALS 1.

    The same thing with 0.999...

    It doesn't "converge to 1" but it is EQUAL to 1.

    1 = 0.999...

    0.999... = 1

    They are one and the same.

    Two different symbols representing ONE number.
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    er... didnt the OP say that ALL of the computer turn on at the EXACTLY same point in time?? well... then it doesnt matter if theres 2 of them or infinity of them. they just ALL turn on at the SAME time...therefore it has nothing to do with convergence theory... after ALL the comps get turned on at EXACTLY the SAME time... time continues on...OP needs to l2logic

    from my understanding convergence theory is when two numbers are real close can be considered the same...this DOES NOT mean dat 2 numbers EXACTLY the SAME(as OP said) are slightly different
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    Originally Posted by Absane View Post
    Well, given two numbers a and b that are real numbers that are not equal, yes, we can say that a > b or b > a.
    0.999... and 1 are not equal

    /thread

    However, you make the assumption, whether you know it or not, that all the real numbers can be listed in some way. As the the mathematician Cantor has shown, one cannot do it. Here you can find a proof: http://www.classy.dk/log/archive/000906.html
    im not making any assumptions, dont try to stick a "wether you know it or not" in there to try to make it seem that no matter what i say your statement will be correct, it isnt, i assume it not
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    Originally Posted by thirsty4chicken View Post
    .999999... to an infinite number of 9's DOES NOT EQUAL 1. It gets infinitely close to 1, but it NEVER reaches 1.

    I'm going to find a math forum somewhere and post a link to this thread so that people can laugh at you.

    May God have mercy on your soul.
    can you cross link it back ?
    kthx
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    Originally Posted by OmniPotentTitan View Post
    0.999... and 1 are not equal

    /thread



    im not making any assumptions, dont try to stick a "wether you know it or not" in there to try to make it seem that no matter what i say your statement will be correct, it isnt, i assume it not
    dood it doesnt make a difference if 0.9999...=1 or not...

    EITHER WAY OP's theory is retarded and does NOT even RELATE to convergence theory... he tried to twist convergence theory to suit sumthing dat is completely irreleveant
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    Originally Posted by OmniPotentTitan View Post
    0.999... and 1 are not equal

    /thread



    im not making any assumptions, dont try to stick a "wether you know it or not" in there to try to make it seem that no matter what i say your statement will be correct, it isnt, i assume it not
    And in your case, your close-minded attitude is the problem. Read through the many links provided by Absane and several others (including me). From your posts, you seem to be a smart person but is just too stubborn.

    http://en.wikipedia.org/wiki/.999

    Start with that link, please. It is fairly simple and there are easy proofs in it.
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    Originally Posted by thirsty4chicken View Post
    .999999... to an infinite number of 9's DOES NOT EQUAL 1. It gets infinitely close to 1, but it NEVER reaches 1.

    I'm going to find a math forum somewhere and post a link to this thread so that people can laugh at you.

    May God have mercy on your soul.
    I'll even link one just for you:

    http://www.physicsforums.com/showthread.php?t=5513
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    i r frozen in time because it doesn't exist! ahhhhhhhhh!
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    Originally Posted by yoda05378 View Post
    And in your case, your close-minded attitude is the problem. Read through the many links provided by Absane and several others (including me). From your posts, you seem to be a smart person but is just too stubborn.

    http://en.wikipedia.org/wiki/.999

    Start with that link, please. It is fairly simple and there are easy proofs in it.
    read through the last 50 posts and you will see quite some nice posts wether by me or others to counter all that mmk ?

    oh and using wikipedia as the one true source of knowledge
    i mean seriously wikipedia, where anyone can edit and place random links to make it look better
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    ALRIGHT!!!! we've figured a way to stop ****in time!!!!

    just get an infinite line of computers and turn them all on at the same time.

    And i'm pretty ****ing sure the first computer will turn on. It takes 5 seconds to do, and after 5 seconds it will be on. The other computers can't sea what each other is doing and decide what they want to do

    /thread
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    i had a question then : how do you disporve that the events at time t = 0 != t = 1
    ?

    so lets say i just typed this post - how can you prove that at a progressive interval time that this post didn't get posted?
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    .999... = 1
    This is wrong. A number less than 1 cannot be 1. Just as a number more than 1 cannot be 1.
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    Originally Posted by OmniPotentTitan View Post
    if you so vehemently believe that there must be a number between 0.999... and 1 then you can see that there is indeed a difference
    I DON'T vehemently believe there is a number beetwee .999... and 1. YOU do. I was asking you to provide one.

    Originally Posted by Joemama06 View Post
    The way I see it.. the seemingly nonexistant difference in time would eventually become noticable if you did this with a million computers. the very small lengths of time would eventually add up to the point where the first computer would have booted up already while say the millionth would not be done booting at the same time. and if there were an infinite number of computers that this occurred with the difference in booting times would just get larger and larger.

    it reminds me of the idea they had in office space to steal money from the company by taking fractions of cents of transactions and putting it into an account. it wouldnt be much at first but over time that would add up to alot of money.
    That would be true if there were "very small lengths of time" to add up, but these "very small lenghts of time" don't exist in my thought experiment. I'm saying the time difference between each event is 0.0 seconds. An infinitely small amount of time is zero, so nothing adds up to anything.
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