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You are not logged in. #26 20120722 14:23:32
Re: Shaking The Foundations Of Mathematics.I am not able to at the moment. I will be able in a few hours, though. 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 #27 20120722 14:57:31
Re: Shaking The Foundations Of Mathematics.Don, 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. #28 20120722 15:16:09
Re: Shaking The Foundations Of Mathematics.
Commutativity is not just the property that we n write it any way we want. It is needed to be stated because all operations are defined on ordered tuples of numbers. 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 #29 20120722 18:31:34
Re: Shaking The Foundations Of Mathematics.
Whoops, my bad haha
The third step (and beyond) is only valid as long as a = b. But you are applying it to cases where a =/= b! #30 20120722 19:52:23
Re: Shaking The Foundations Of Mathematics.To: noelevans,
I agree. without knowing the circumstances under which it occured. In and of itself, can be any number because just as implies the true statement , implies the true statement while implies the false statement . From my point of view, since implies a true statement, the symbol can be used to make other true statements. can indeed be construed as meaning "one raised to any power equals one". Don. #31 20120723 00:20:04
Re: Shaking The Foundations Of Mathematics.Hi Don Blazys 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 #32 20120723 02:06:42
Re: Shaking The Foundations Of Mathematics.I agree, and first stated that with a little false proof that should be well known in post #6 +. 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. #33 20120723 02:15:36
Re: Shaking The Foundations Of Mathematics.I saw it. But apparently Don Blazys didn't. 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 #34 20120723 20:46:05
Re: Shaking The Foundations Of Mathematics.
That is harsh and argumentative. 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. #35 20120723 22:21:01
Re: Shaking The Foundations Of Mathematics.So it isn't a number, obviously. 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 #36 20120725 16:40:18
Re: Shaking The Foundations Of Mathematics.So clearly, we all agree that division by zero is strictly disallowed.
it's not always true that "if then ",and we can't always substitute for . Don #37 20120725 22:49:45
Re: Shaking The Foundations Of Mathematics.We can substitute a/a with b/b ! You have illegal steps in your work! 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 #38 20120726 16:15:40
Re: Shaking The Foundations Of Mathematics.
I'm not sure how he made any changes to the function in his work. You have been stating that he has made an error by subtracting 1 from the numerator and the denominator when clearly he followed the properties of logs.
His overall argument (if he would have put in those extra restrictions which avoids 0/0) reminds me of set theory. This makes sense in a way why Don Blazys' argument doesn't work for a = 0 and thus b = 0, because the empty set does not have the possibility of being a proper subset of itself: . But then again, what about the next natural question that follows: Is (because he claims that ). Certainly this cannot be true, but what happens if we exclude the empty set from set theory? The definition of a set would change... So maybe that's where this argument might be headed... Very interesting argument for nonzero a (and thus nonzero b), which is a big chuck of the reals if you ask me! I know very little about set theory, so maybe someone could add on to this/point out some things I said which might be incorrect about set theory. Last edited by cmowla (20120726 16:19:00) #39 20120726 18:51:22
Re: Shaking The Foundations Of Mathematics.Hi cmowla Hi Don Blazys This step is flawed:
You cannot have a 0 in the denominator of a fraction. ln(a^3/b) and ln(a/b) are both 0,so that is the flawed step. You turned a 3 into 0/0. Last edited by anonimnystefy (20120726 18:56:20) 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 #40 20120727 02:38:36
Re: Shaking The Foundations Of Mathematics.Hi anonimnystefy,
I know. I said "It reminds me of" set theory, not that it "is". I was giving a comparison and trying to brainstorm a way to try to interpret how this result can be explained. Set theory is not completely solid (paradox), so I thought I could make a comparison (not that they are equal).
How is either zero? unless (which he clearly gave as a restriction). If then that just makes the entire exponent zero. That is, because . And since he wrote , then a and b cannot be zero...but that's the only restriction. Also, look at this: So between this and what I said earlier in this post, I cannot see where the errors are. Please don't say (0/0) again unless you can show how that happens, GIVEN THE RESTRICTIONS I gave in this post. #41 20120727 03:04:59
Re: Shaking The Foundations Of Mathematics.Hi cmowla 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 #42 20120727 03:27:39
Re: Shaking The Foundations Of Mathematics.Hi, anonimnystefy,
I ask kindly that you show your reasons (in fact, I asked in my last post for you to explain yourself).
The starting assumption was: This equality is true whether a = b or a does not equal b. As long as a and b are nonzero, it's a true statement. And yes, there is a contradiction when he wrote (and, as I have said several times already, for nonzero a and b). ...because he cleverly made one which works for nonzero a and b. That contradiction is the core of his argument. So, unless I have not fully identified what you found as incorrect yet, the only portion of his argument that was incorrect was that he didn't mention that a and b must be nonzero (which was pretty obvious to me, even though he didn't state it). Last edited by cmowla (20120727 03:28:40) #43 20120727 03:41:10
Re: Shaking The Foundations Of Mathematics.Also, I forgot to comment on what you were actually implying when you wrote:
A 3 into (0/0)? The exponent should be a 3? Nope. It's a/b raised to the exponent. Not . It's not obvious why he chose to start with b(a/b)^x = a^3, where we can algebraically solve for x (as I did in my last post), but it works out nicely. #44 20120727 03:55:00
Re: Shaking The Foundations Of Mathematics.
This is the flawed step. He turned an exponential with base a^3/b to an exponential of the form 1^(log_1(...)) (which is "against the rules") and then turned that into a fraction using logarithm rules. 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 #45 20120727 06:09:36
Re: Shaking The Foundations Of Mathematics.
Can you explain why it's against the rules? If it means anything, (a/b)^(Log[a^3/b]/Log[a/b]) = a^3/b with Mathematica. #46 20120727 06:19:44
Re: Shaking The Foundations Of Mathematics.Don't you see the difference in the graphs? There is a weird (x=y) line on the second graph. 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 #47 20120727 08:03:34
Re: Shaking The Foundations Of Mathematics.
Obviously you don't read everything in my posts...
You didn't comment at all about the result Mathematica gave? And because x cannot equal y in the 3D graph, this just explains his restriction that a cannot equal b. But the work from Mathematica proves that he did not make an error when expressing a^3/b with logs. #48 20120727 10:57:10
Re: Shaking The Foundations Of Mathematics.I think nobody could shake the fundamental of mathematics. The reason why all seem working is because of the division by zero is ignored. The concept of proving 2=1 also ignores the division by zero. This is why when you have statement like a=b and the derivation of the equation consist of expression that leads to the division by zero then the statement a=b must be not true in the first step. Consider this, a=b, multiplying both sides by a we get a^2=ab and minus both sides by b^2 yields, a^2b^2=abb^2=> (a+b)(ab)=b(ab)=>a+b=b and a=b, thus 2b=b=>2=1. Anything leads to the division by zero through ab or ln(a/b) must not be true in the beginning when it is stated a=b. #49 20120727 16:21:56
Re: Shaking The Foundations Of Mathematics.To: cmowla, #50 20120727 18:11:44
Re: Shaking The Foundations Of Mathematics.
The equations are not both true!!! Have you read my post above. I have clearly shown why it is not true and you still go on and on about how mathematics is flawed. You have just done something that is bot allowed and that resulted in something that is frobidden in mathematics. This also shows clearly that you have no intention of discusing this matter properly as you didnt even think about reading and replying to my last post explaining why your argument is flawed and not math. 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 