0.99999~ = 1 ?

You won a math debate...read aloud for the lulz

Huh? Sorry, you lost me.But it does remind me of when we had a crowd of 5000, all politely arguing separate points of view. Ah, the joys of mass debating...Now, what were you talking about?

it sounds like 'you wanna masturbate'did you not read it out loud?Edited by Catholic Scientist, : No reason given.

Yes, but you obviously didn't read my reply

ahhh, mass debating.heh, yeah, I missed that >.<

Mass debating belongs in a religion thread.

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You are now a million miles away from where you were in space-time when you started reading this sentence.

Hi cavediver, it may just be a mathematical semantic thing. This also holds for all the frame shift proofs as well.I'm aware that functionally they are similar, I just find them conceptually different, as one seems (unnecessarily) more manipulated than the other, and it seems that the main argument is about how you phrase the problem, rather than the actual solutions.My dad makes a comment about mathematicians understanding the problems very well, but not understanding how to communicate their understanding to those who do not understand maths, so I try for the simplest paths possible.It's quite interesting to see the variety of ways people have gone about this, and I'm rather astounded that this thread has persisted so long.It might be interesting to see how people think which explanations are the ones that best convince them -- Huntard and Straggler and any other lurkers who had trouble with this issue.enjoy.

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Mmm ... not really. But that's not what's happening.Look, call 0.9999~ x.Then we have (1+x)/2 = x.So 1 + x = 2xi.e. 1 + x = x + x.So 1 = x.

RAZD writes:

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In the process it uses another version of 0.999~

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Incorrect.In the process, it calculates that (1 + 0.999...)/2 = 0.999.... This can only be true if 0.999... = 1.Are you saying that (1 + 0.999...)/2 does not result in a pair-wise identity in each decimal place with 0.999...?Let us not play dumb.

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One can't use the conclusion as part of the proof eh?

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And if that were the case, you might have a point. But instead, we are finding that a calculated value (the quotient) is identical to the constant we used. And because of that, in the context of the proof, this means that 0.999... = 1.(x + x)/2 = xThat second "x" is a calculated x, yes, but that's the point of the proof. Because if (y + x)/2 = x, then y = x.So we start with y = 1 and x = 0.999... and then do a calculation on it. If we wind up with 0.999..., then we know that y = x and 1 = 0.999....Are you denying that (1 + 0.999...)/2 = 0.999...?

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A much simpler process is take 0.999~, multiply it by two (=1.999~), where the 9's are exactly aligned from the decimal, and subtract the original ( 1), QED

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It isn't "simpler."It's backwards.Your method also works since identities are isomorphic and thus the implications go both ways [(A=>B) => (B=>A)], but it is hardly simple for it requires the exact same process: Performing a mathematical operation upon an infinite decimal.You have the exact same problem you are complaining about: What makes you think the 9s in 1.999... are the same as the 9s in 0.999...?Easy: The mathematical operation is correct and the notation shows it to be so.Whether we add and then divide or we multiply and then subtract is immaterial.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

Jazzns writes:

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Yea transcendentals are contained in the irrationals.

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Yeah. The Rationals are simply defined as the set of numbers that can be expressed as a/b where a and b are Integers. The Irrationals are those numbers that cannot be expressed that way.Thus pi, e, and the square root of 2 are all irrational.Transcendental numbers are those that aren't algebraic, meaning roots of a polynomial equation with rational coefficients. The square root of 2 is algebraic, but pi and e aren't.And there is the constructible dichotomy: Those numbers which can be constructed via straightedge and compass are "constructible" while those that can't aren't. The square root of 2 is constructible, pi is not. And that's why it is impossible to square the circle: The square root of pi is not constructible.All constructible numbers are algebraic, but not all algebraic numbers are constructible. All rational numbers are constructible, but not all constructible numbers are rational.There are all sorts of ways to divide the real numbers down. That's part of the reason that Real Analysis is so fascinating: There are just so many numbers and with different properties to them that you can divvy them up any which way and learn all sorts of interesting things about the way numbers can behave.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

RAZD writes:

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I'm aware that functionally they are similar

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It is more than just "similar." They are identical. This is part of the reason why in the proof that the Reals are uncountable that you have to choose the notation of the repeated decimal format.

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I just find them conceptually different, as one seems (unnecessarily) more manipulated than the other, and it seems that the main argument is about how you phrase the problem, rather than the actual solutions.

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And yet, as I have pointed out more than once, there is at least one problem that hinges upon this equivalency.There are plenty of things in physics that make absolutely no sense intuitively and yet we know they are true. We run the experiments and we get results that only make sense if the world works in ways completely against what we would normally expect. The very idea that no, you can't go faster than the speed of light is one of them. A car going at 40 miles an hour crashes headlong into a car coming toward it at 50 miles an hour. Their combined force impact is NOT equivalent to the single mass of both cars crashing into a stationary object at 90 miles an hour. Relativistic effects are present at all levels. The only reason we didn't figure it out sooner is because the effect is so small that we didn't notice it. Now that we can mover faster and farther, those effects become more noticeable.Mathematics is the same way: Some things don't seem right but they are and unlike physics, you can actually prove it forever to be true.

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My dad makes a comment about mathematicians understanding the problems very well, but not understanding how to communicate their understanding to those who do not understand maths, so I try for the simplest paths possible.

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The thing is that just like physics and biology, the really interesting questions don't have simple answers. There's a reason that it takes over 60,000 steps to prove that 1 + 1 = 2 from first principles. It took Russell and Whitehead years to develop the proof and Russell nearly went mad over it. There are plenty of pithy phrases we can say, but to be rigorous about it requires that we abandon pretenses of simplicity and admit that it's hard work to understand this stuff.

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Rrhain

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Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

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Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

What is it about math that makes people go mad, anyway? Or is it simply mad people that practice math?

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I hunt for the truthI am the one Orgasmatron, the outstretched grasping hand
My image is of agony, my servants rape the land
Obsequious and arrogant, clandestine and vain
Two thousand years of misery, of torture in my name
Hypocrisy made paramount, paranoia the law
My name is called religion, sadistic, sacred whore.
-Lyrics by Lemmy Kilmister of Motorhead

Hey RAZD,Is my proof incorrect or to you just think it's unnecessarily complicated? If it is the latter, what in particular do you find unnecessary. It's always good to know where explanations can be improved.

Well, seriously, I don't think it's particularly an occupational hazard any more than for painters or poets or what-have-you.But even then, I don't think that it's particularly a hazard for creative people. Psychologists used to call schizophrenia "truck-drivers' disease". Madness doesn't particularly strike down the highly creative, it's more that highly creative people are far more likely to have someone write their biographies. You are far more likely to find out that your favorite physicist has spent time in a mental hospital than you are to find out that the clerk at your local grocery store has done so, because no-one is prying into the life of the latter.I remember when I stopped reading biographies of famous men. It was when I read a biographer of C. S. Lewis write that there was "no evidence" that his marriage was ever consummated. What did he want, a bloody sheet?Um ... I've gone far enough off topic, I'll shut up now.

Well I was convinced of the wrongness of my initial intuitive assertion pretty much straight away. Just looking at what others had written and thinking about it a bit convinced me of that on a rational level. I just didn't like it. It didn't feel right. I pursued the matter to A) Try and explain why I thought intuition and fact were so at odds B) To find a way of reconciling the two in my own head.I think I achieved both (to my own satisfaction anyway) by thinking of this in terms of an infinite series and asymptotes. As per Message 79All of which Mr Jack had been saying to me in so many words anyway. It was just this particular approach/phraseology that made the penny drop in my own intuitive head.