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You are not logged in. #1 20120716 20:29:23
Shaking The Foundations Of Mathematics.The "foundations of mathematics" are its axioms, which are defined as "self evident truths". Well, if where , and the properties of logarithms allow where , then clearly, that so called "symmetric axiom of equality" is neither self evident, nor always true! Don. #2 20120716 22:38:03
Re: Shaking The Foundations Of Mathematics.Can you show the steps you took to get from to It's not obvious to me how you do that. Wrap it in bacon #3 20120719 09:28:31
Re: Shaking The Foundations Of Mathematics.
You are dividing by zero in your exponent, so there must be something wrong here Your problem is at the third step. The fraction is equal to 0/0 and thus no longer equals the value in the second step. #4 20120722 04:04:12
Re: Shaking The Foundations Of Mathematics.Quoting MrButterman
That is not true. I am not dividing by zero. In fact, I am doing exactly the opposite! which means that substituting for is strictly disallowed, because division by zero is strictly disallowed. This is an extraordinarily serious issue because if the symmetric axiom of equality is flawed, then the substitution axiom of equality, which states that we can "always" substitute for is also flawed! Quoting MrButterman:
At , your equations contain the removable singularity which is so utterly trivial that we mathematicians refer to it as "cosmetic".In this particular case, since the expression at by definition . Thus, in this particular case, that indeterminate form , so at , your third step is clearly equal to your second step. By contrast, at , my equation has a nonremovable singularity which demonstrates that some axioms are not always true! Quoting MrButterman:
What's wrong here are those badly flawed axioms, which when taught to unsuspecting students, #5 20120722 04:23:31
Re: Shaking The Foundations Of Mathematics.Could you reply to TheDude's question in post #2? 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 #6 20120722 04:58:59
Re: Shaking The Foundations Of Mathematics.Hi Don; So, dividing by 0? replacing 0 / 0 by the assumed identity 0 / 0 = 1 so 1 = 2? It is clear that the culprit is the asumption 0 / 0 = 1 in the arithmetic sense. 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. #7 20120722 05:55:12
Re: Shaking The Foundations Of Mathematics.To: TheDude,
The "Blazys identity" is derived as follows: Note that it is not possible to derive this identity if the coefficient of the first term is either or simply . Don. #8 20120722 06:00:03
Re: Shaking The Foundations Of Mathematics.Hi
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 #9 20120722 06:22:34
Re: Shaking The Foundations Of Mathematics.To: anonimnystefy,
All the steps are correct, including that one. #10 20120722 06:44:23
Re: Shaking The Foundations Of Mathematics.No. that one is not correct. There is no explanation for subtracting ln(b)/ln(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 #11 20120722 06:56:49
Re: Shaking The Foundations Of Mathematics.To: bobbym,
I agree. Care must be taken and we can't just let the indeterminate form .We must first know the details of how it occured in order to give it a specific value. For instance, in the expression , we know that if we let approach , then . Thus, we can define at as being . Don. #12 20120722 07:00:23
Re: Shaking The Foundations Of Mathematics.Hi Which is not true! When we define division, we don't allow 0 to be the second argument. 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 #13 20120722 07:03:49
Re: Shaking The Foundations Of Mathematics.Hi; 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. #14 20120722 07:38:39
Re: Shaking The Foundations Of Mathematics.In the field axioms the multiplicative inverse axiom does not allow for zero to have a multiplicative inverse: Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #15 20120722 08:12:44
Re: Shaking The Foundations Of Mathematics.Regarding the statement that Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #16 20120722 08:16:45
Re: Shaking The Foundations Of Mathematics.Hi noelevans Code:[math][/math] to display it. Last edited by anonimnystefy (20120722 08:17:08) 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 #17 20120722 08:21:37
Re: Shaking The Foundations Of Mathematics.In complex analysis, if we can't define as being at ,then neither can we define as being 1 at . Let's all Google the phrase "removable singularity" and find out! Don #18 20120722 10:04:27
Re: Shaking The Foundations Of Mathematics.We can certainly define a function f(x)=x/x by f(x)=1 if x<>0 and f(x)=a (a any real number) if x=0. And it is certainly nice to define this as 1 since this is the limit of the function as x approaches 0. Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #19 20120722 10:28:07
Re: Shaking The Foundations Of Mathematics.
No one defined sin(x)/x to be 1. The limit of that expression is 1 when x approaches 0. Same for x/x. It is indeterminate and undefined at 0 but its limit as x approaches 0 is 1. 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 #20 20120722 11:13:37
Re: Shaking The Foundations Of Mathematics.To:anonimnystefy,
Quoting the article "Removable singularity" from Wikipedia:
Please note the phrase "removed by defining".
It's not a formula. It's an identity, and it's correct. #21 20120722 11:19:21
Re: Shaking The Foundations Of Mathematics.Yes, we could define another function partially, so that it has no singularities, but that wouldn't be the same function we started with. 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 #22 20120722 13:17:00
Re: Shaking The Foundations Of Mathematics.stefy, Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #23 20120722 13:32:04
Re: Shaking The Foundations Of Mathematics.Quoting anonimnystefy:
Please look carefully.
That's kind of like saying that after somebody "pops a zit", they don't have the same face they started with. while MrButtermans equations have a removable singularity at . Therefore my identity presents a much stronger argument for eliminating the symmetric and substitution axioms of equality. However, if you want to join my crusade to eliminate those shoddy axioms using MrButtermans much weaker equations, then I still welcome your support because really, those axioms have got to go. Don #24 20120722 13:54:39
Re: Shaking The Foundations Of Mathematics.Hi 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 #25 20120722 14:21:36
Re: Shaking The Foundations Of Mathematics.Hi,
Can you post the above in LATEX? I'm sure that our readers will appreciate it! 