Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #51 20120727 18:37:29
Re: Shaking The Foundations Of Mathematics.Your posts aren't even in LATEX. cmowla's "Mathematica" results are clear. You are simply wrong! #52 20120727 18:54:00
Re: Shaking The Foundations Of Mathematics.Just because my posts aren't in LaTeX implies tgat I am wrong? That is truly false logic. Last edited by anonimnystefy (20120727 18:56:32) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #53 20120727 19:21:44
Re: Shaking The Foundations Of Mathematics.That your posts aren't even in LATEX shows that you can't #54 20120727 19:30:32
Re: Shaking The Foundations Of Mathematics.No, it just implies that I am on my phone. If I was on my computer like I am now, I would be glad to LaTeX anything that needs LaTeXing. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #55 20120727 19:35:41
Re: Shaking The Foundations Of Mathematics.Which of course proves my point! #56 20120727 19:38:09
Re: Shaking The Foundations Of Mathematics.No it doesn't. Did you look at post #44? Can you comprehend it correctly? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #57 20120727 19:43:02
Re: Shaking The Foundations Of Mathematics.Yes, I comprehend it perfectly. It shows that you are wrong. #58 20120727 19:52:28
Re: Shaking The Foundations Of Mathematics.
This is the post I am talking about. It shows that you are wrong. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #59 20120727 19:59:58
Re: Shaking The Foundations Of Mathematics.That's an identity, pure and simple. You are wrong. #60 20120727 20:08:01
Re: Shaking The Foundations Of Mathematics.It is not an identity. It is an identity when a<>b. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #61 20120727 20:08:53
Re: Shaking The Foundations Of Mathematics.I am sorry fellows but at the beginning of a similar thread I warned everyone involved that name calling and fighting will not be tolerated. This thread is closed until tempers cool. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #62 20120801 15:23:40
Re: Shaking The Foundations Of Mathematics.The thread is reopened for posting. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #63 20120801 17:21:45
Re: Shaking The Foundations Of Mathematics.Quoting anonimnystefy:
Quoting anonimnystefy (one post later):
Well, if it's an identity, then there can be no "flawed step". #64 20120801 21:35:29
Re: Shaking The Foundations Of Mathematics.It is flawed because you assumed in the begnning that a=b. The identity doesn't hold when a=b. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #65 20120802 10:22:50
Re: Shaking The Foundations Of Mathematics.I agree with anonimnystefy. You should put the condition at the end and not at the beginning because you know at the end the condition is not valid, implying it is not valid through out the derivation. In other words, it is wrong to put a=b in the first place. You should refer to the flaw proof of 2=1 when it is assumed at the beginning that a=b. #66 20120802 15:46:39
Re: Shaking The Foundations Of Mathematics.Quoting anonimnystefy:
That's what I said in the opening post of this thread! we can never let or substitute for even though those so called "axioms of equality" say we can? Don #67 20120802 23:05:11
Re: Shaking The Foundations Of Mathematics.The axioms of equality do not say we can do that. The axioms of equality never mention logarithms in the first place. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #68 20120803 20:07:04
Re: Shaking The Foundations Of Mathematics.Quoting anonimnystefy:
Of course they do! Take for instance the substitution axiom of equality which states that but if we try to replace with in the identity , then we quickly find that it's quite impossible, because clearly, the above identity has thoroughly and irrevocably negated the closely related symmetric axiom of equality which states that if , then . Now, this is not the first time that a faulty axiom has been negated by a perfectly logical mathematical construct. We must not forget that the negation of Euclids fifth axiom (parallel postulate) ultimately resulted in many vastly superior "nonEuclidean" geometries, one of which even allowed Einstein to formulate his theories of relativity! Don. #69 20120803 21:56:22
Re: Shaking The Foundations Of Mathematics.The substitution cannot be done because the of the restrictions that the lofarithms pose. The "identity" works for a<>b, so substituting a=b is flawed. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #70 20120804 18:21:50
Re: Shaking The Foundations Of Mathematics.Quoting anonimnystefy:
You see folks, that so called "substitution axiom of equality", has been debunked by the rather simple counterexample . We can not allow that utterly ridiculous "axiom" to be shoved down our children's throats! Don #71 20120804 19:32:28
Re: Shaking The Foundations Of Mathematics.I never said you cannot substitute a/a with b/b. Your further steps are incorrect. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #72 20120805 08:00:51
Re: Shaking The Foundations Of Mathematics.Sorry Don, but even though (where ),Your whole argument is redundant. Let me explain. (Notice that it IS possible for , and that's why I added that important detail in). Since we have as well as , then your logarithmic function (if we choose not to simplify it to ) just illustrates a case where the condition holds. The 3D graph of your log function is different than the 3D graph of , but that has nothing to do with the validity of your argument (it is neither for you nor against you) because the conditions for the values of and are not different (you just left out the fact that a can also not be equal to b in your first equation without the logs). Here's a polynomial function which shows where the condition must hold: This supports the other possibility that a can be equal to b (a must be equal to b, that is...just as in your log function where a must not be equal to b....and we are assuming that we don't simplify our functions completely to (b/b)a^3). An even more trivial case (which you probably thought of but didn't post) for when a must not equal b is: and so suppose we have: Again, the graph of and are different, but they do not disagree with the conditions. How could they? They are equal expressions once you simplify the more complicated one into the simpler one. Last edited by cmowla (20120805 10:40:08) #73 20120805 16:48:26
Re: Shaking The Foundations Of Mathematics.Given the identity: can we substitute for ? Please just answer yes or no without any commentary. Don #74 20120805 18:05:03
Re: Shaking The Foundations Of Mathematics.That is not an identity when a=b. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #75 20120805 18:18:55
Re: Shaking The Foundations Of Mathematics.Please just answer yes or no without any commentary whatsoever. 