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| Posted By: Pyrovus Posted On: Mar 6, 2005 Views: 357 | RE: Dumb Thought/Question I have Hi all, Quote: "You made a fatal mistake in your theory. 1 != .999999999' As we learn from derivatives and anti-derivatives, every time you derive you either lose a constant or add one (+ C). You failed to account for this. Your answer should be: 3x^2 = 6x, but the anti-derivative of 6x = 3x^2 + C" Interesting, but I did not use derivatives in my proof, which makes this objection irrelevant. I assume you're referring to this? Lim n->infinity 1/10^n = 0 This involves asymptotes, not derivatives, and 0 is the only answer. Draw the graph if you don't believe me. Let's just for the sake of argument, assume that everything I've said is rubbish, and that the difference between 1 and .999999' is not 0. In that case 1/(1-.9999') should give a single, clearly defined finite answer (as opposed to 1/0 if 1 and .9999' are the same). So, all you need to do to prove that .9999' doesn't equal 1 is to find that number. Good luck. |
| Posted By: Keith Mayes Posted On: Mar 6, 2005 Views: 352 | RE: Dumb Thought/Question I have Pyrovus, I really can't understand why you have such a problem with this. At the risk of, as we say in the UK, of "stating the bleeding obvious" allow me to make one final attempt to clarify it fo you. 1 is a whole number. Therefore any decimal expression of a number that begins with 0 is, by definition, less than 1. No calculation, formula or theory can alter that. There is only one number that is equal to 1, and that is 1. If you still have a problem with that I have to say that I am unable to help you. Take it up with someone else. |
| Posted By: Pyrovus Posted On: Mar 6, 2005 Views: 348 | RE: Dumb Thought/Question I have Are you actually able to come up with any arguments to refute my position? Simply asserting that "no calculation, formula or theory can alter" the "fact" that .999' =/= 1 when confronted with a proof that .999'=1 is not exactly the most persuasive argument. |
| Posted By: Alan Posted On: Mar 7, 2005 Views: 338 | RE: Dumb Thought/Question I have MY HEAD IS STARTING TO CRACK, STAND BACK THERES ABOUT TO BE A BLOODY EXPLOSION! |
| Posted By: Keith Mayes Posted On: Mar 7, 2005 Views: 336 | RE: Dumb Thought/Question I have Do I need an argument to prove that 2 is less than 3? No, it's a given. Do I need an argument to prove that 0.99999' is less than 1? No. it's a given. Any number expressed as a decimal that begins with 0. is less than 1. That argument is undeniable. (Zero being less than one in case you didn't know) As I have already said, if you are unable to appreciate that very simple mathematical fact, then you have a problem. A problem that I can't help you with. |
| Posted By: Pyrovus Posted On: Mar 7, 2005 Views: 331 | RE: Dumb Thought/Question I have Quote: "Do I need an argument to prove that 2 is less than 3? No, it's a given. Do I need an argument to prove that 0.99999' is less than 1? No. it's a given." That's like saying "do I need an argument to prove that the Earth is the centre of the universe when IT HAS JUST BEEN PROVEN OTHERWISE? No, it's a given." When we are confronted with evidence that one of our assumptions is false, there are two possibilities. The first is to revise our assumptions in the light of new evidence. The second is to blindly reject the new evidence, and let nothing change our original assumption. You seem set on the latter option - basically saying "I don't want to believe .999'=1. Maths says .999'=1. Therefore maths is wrong." Funny, really, since in your site you gave the impression of being more open minded than that. Why don't you ask a few mathematicians? It is a mathematically accepted fact that .999'=1, which every first year maths student knows. If you are unable to appreciate that very simple mathematical fact, then you have a problem.You could also try going to www.physicsforums.com - there's quite a few threads on the .999'=1 subject in the maths section. |
| Posted By: Keith Mayes Posted On: Mar 8, 2005 Views: 326 | RE: Dumb Thought/Question I have My saying that 2 is less than 3 is not an assumption it is a mathematical fact. Or do you intend to challenge that as well? Comparing that to the the false assumption that the earth was once believed to be the centre of the universe is pointless, it has nothing to do with this argument. The progession of higher value numbers is not based on assumptions but on mathematics. As I said before, I have no interest in what theories you may belief 'prove' that 0.999999' is equal to 1 for one very simple reason, which is any number beginning with zero has to be less than any number beginning with 1. (Zero being less than 1) Therefore any theory that claims othwerwise is wrong, because the very basis on which mathematics is derived rests on that very simple concept, 0.(anything) is less than 1.0 You may as well show me a theory that 'proves' that 1+1=3. Would I believe it? No. of course not. Would I need to be more open minded about it? No, of course not. Would I need to study the theory and consult with mathematicians? No, of course not. The same goes for does 0.9999' equal 1. Of course not. That decimal, BY DEFINITION is less than 1. It no more is equal to 1 than 0.5 is, it is closer to 1, but isn't 1. |
| Posted By: Pyrovus Posted On: Mar 8, 2005 Views: 320 | RE: Dumb Thought/Question I have Quote: "As I said before, I have no interest in what theories you may belief 'prove' that 0.999999' is equal to 1 for one very simple reason, which is any number beginning with zero has to be less than any number beginning with 1. (Zero being less than 1) Therefore any theory that claims othwerwise is wrong, because the very basis on which mathematics is derived rests on that very simple concept, 0.(anything) is less than 1.0" So, basically you're rejecting addition, multiplication, infinite sums, limits, and, as calculus funtions are defined by limits, all of calculus. My proofs rely only on the assumptions that these are valid operations. If you want to believe in a mathematical system without them, go ahead, but it's not going to be terribly useful. Honestly, what's wrong? 1 is defined as being 1/3 x 3. .9999' is also defined as being 1/3 x 3. Is it really so shocking that they should happen to be the same number? Your entire case seems to centre on the fact that .999' and 1 LOOK different. I ask you, which is more reasonable to believe? That multiplication and division work differently dependent on the way you write the numbers, or that our number system has a curious quirk that causes there to be two different ways for writing the same number. So, which is flawed? Mathematics or notation? Quote: "Comparing that to the the false assumption that the earth was once believed to be the centre of the universe is pointless, it has nothing to do with this argument." It's called an analogy. I'm simply showing that you're using the same reasoning that people such as modern-day geocentrists use when confronted with evidence conflicting with their dogma - blind rejection. Quote: "Would I need to study the theory and consult with mathematicians? No, of course not." What's the harm in checking with those who do know the theory? Is it the risk that they might disagree with you? Just for fun, I've got a little reductio ad absurdum proof which I did this morning, showing that the belief that .999' |
| Posted By: Pyrovus Posted On: Mar 8, 2005 Views: 317 | RE: Dumb Thought/Question I have Sorry, the software seems to have cut off the last bit of my post. I've got a tutorial to go to now, so I don't have time to re-write it now. I'll be an hour or so (for anyone wondering why it suddenly cuts off). |
| Posted By: Pyrovus Posted On: Mar 8, 2005 Views: 314 | RE: Dumb Thought/Question I have Ok,I'm back - ignore the last post. So, I'll continue from where the computer cut off :(. Just for fun, I've got a little reductio ad absurdum proof which I did this morning, showing that the belief that .999'=1 is self contradictory. So, we'll start by assuming that .999' |
| Posted By: Pyrovus Posted On: Mar 8, 2005 Views: 311 | RE: Dumb Thought/Question I have Hmmm . . . this computer seems to have a grudge against me - cutting off posts after a few lines. I'll try again from my home computer, rather than chop the message up into 20 seperate pieces. Sorry about this. |
| Posted By: Pyrovus Posted On: Mar 8, 2005 Views: 308 | RE: Dumb Thought/Question I have Looking at where it cut off my posts the previous times, it appears do do so wherever a greater than or less than sign is used. So I'll be using [ to mean less than and ] to mean greater than. So, anyway, we'll start by assuming that .999' [ 1. Now, we'll use averages. For any 2 real numbers, a and b, such that a [ b, there exists a number (a+b)/2 (the average), such that a [ (a+b)/2 [ b (or in other words, the average of 2 numbers is greater than the smaller one but less than the greater one) So, letting a=.999' and b=1, we can now calculate the average: (a+b)/2 = (.999' + 1)/2 = .999'/2 + 1/2 = .4999' (simple short division) +.5 = .999' Now, remember that a [ (a+b)/2 [ b hence .999' [ .999' [ 1 So, .999' is less than itself! Oh dear. And it gets better: .999' [ .999' therefore .999' + c [ .999' + c So every number is less than itself - or to put it more plainly, no number is equal to itself. But there's more fun to come! Going back to our original calculation of the average, for which our answer is .999', we find that this happens: (.999' +1)/2 = .999' :. .999' + 1 = 2x.999' :. 1=.999' (surprise surprise) BUT this contradicts our original assumption that .999' [ 1. So the belief that .999' is less than 1 is self refuting - if it's true, then it's false. So, in order to believe that .999' [ 1, and for your beliefs to be consistant, you must also believe: - That no number is equal to itself - It is possible for two mutually exclusive statements to be true at the same time Your choice. |
| Posted By: Keith Mayes Posted On: Mar 9, 2005 Views: 304 | RE: Dumb Thought/Question I have Pyrovus, Looking at the way you present your mathematical 'proof' it is no wonder that you think your equations prove that 0.9999' is equal to 1. Stop being silly and look at the facts. 0.(anything) is less than 1.0 by definition. What could be more obvious? Zero is less than one, no matter what digits or mathematical symbols are placed after the decimal point, it doesn't alter the obvious and basic mathematical fact that zero is less than 1. If you think you manage to show otherwise then that only demonstrates that your argument is seriously flawed, which it is. I am not wasting any more time on this, it is too foolish to pursue. Take it with someone who thinks your argument makes sense, if such a person exists. Thread closed. |
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