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You are not logged in. #1 20121108 17:03:19
Continuous FunctionsNew page: Continuous Functions "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20121108 17:23:03
Re: Continuous FunctionsHi MathsIsFun, Character is who you are when no one is looking. #3 20121108 17:56:55
Re: Continuous FunctionsHi MIF! 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. #4 20121108 18:29:00
Re: Continuous FunctionsHi MIF; 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. #5 20121108 19:44:22
Re: Continuous Functionshi MathsIsFun, Is that really undefined at x = 1 ? I'm not sure about the answer to that. You can say it isn't defined there in the definition, or you could define it to be 2, but it's unclear. There are lots of situations where we simplify and then substitute after (eg. calculus). This function obeys the continuous definition requirement at x = 1. I accept the point about 0/0 but this example may nevertheless cause controversy amongst your readers. Suggestion: Replace with Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20121108 20:50:53
Re: Continuous FunctionsHi bob bundy; 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 20121108 21:19:15
Re: Continuous FunctionsYes, this gets me every time, too. It is just so natural to simplify, how can it be wrong? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #8 20121108 23:54:11
Re: Continuous Functionshi MathsIsFun and bobbym,
It's all in the definition of the domain.
There have been several posts recently that seem to suggest that once you have been told the equation for the function then the domain follows of its own accord. I disagree. I think that the domain is part of the definition and hence it's up to the definer to declare whether the domain is changed. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #9 20121109 00:36:06
Re: Continuous Functions
Those functions are not continuous, but the sinvularities they have are removable. Try searching removable singularities. I think there is a Wikipeadia article on it. 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 #10 20121109 00:56:13
Re: Continuous FunctionsThere is: You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #11 20121109 01:25:12
Re: Continuous FunctionsExcellent! I have discovered a truly marvellous signature, which this margin is too narrow to contain. Fermat Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes Young man, in mathematics you don't understand things. You just get used to them.  Neumann #12 20121109 01:58:45
Re: Continuous FunctionsHi Bob Last edited by anonimnystefy (20121109 02:01:12) 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 20121109 12:37:13
Re: Continuous FunctionsHmm, I'm honestly a little bit confused about 1...indirect thing. Is 0/0 really undefined? I would have honestly thought it equals 0. I'm a little bit confused on that one part, so anyone care to explain (why 0/0 is undefined)? Though I do understand why it's not a continuous function. Other then that, I'd say you explained things clearly enough to be able to understand everything, so I'd say you did a pretty good job. Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #14 20121109 13:30:04
Re: Continuous FunctionsHi Calligar; 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. #15 20121109 16:59:32
Re: Continuous FunctionsIf you are talking about the 3'rd line where it says, (ab)(a+b) = b(ab), you are multiplying, not dividing, unless I'm missing something...? Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #16 20121109 19:17:20
Re: Continuous Functionshi Calligar You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #17 20121110 02:07:19
Re: Continuous FunctionsHi Calligar;
In line three you have a factor of (ab) on both sides. On line 4 you do not. Both sides were divided by (ab) which is equal to 0. That is the misstep. Generally, you never divide by a variable unless you are sure that it cannot be 0. Sometimes such divisions are fatal, sometimes they just destroy answers. For instance Divide both sides by x Here the decision to divide by x, has cost us the other root which is 0. 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. #18 20121110 08:01:45
Re: Continuous FunctionsNice extra example bobby. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #19 20121110 14:22:45
Re: Continuous FunctionsHi! 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. #20 20121112 09:56:39
Re: Continuous FunctionsOkay, I understand the fact that you can not divide x by 0, but i was strictly talking about 0 / 0, not 1, 2, or any other number. I don't understand why you can't divide by 0 in that case, because I do see 0 x 0 = 0 if u changed it to multiplication. Also, I didn't realize that rule applied to 0 as well, that was why I was asking. I already knew about stuff like 1/0 is undefined though and already understand why that is. Also I have read every post, and it still doesn't seem to prove to me that 0 / 0 is undefined, maybe because I'm looking at it the wrong way? Though I also worry about arguing this further, as this might only end up being something just like 0.999...=1. So, I'm just going to assume its a rule right now I don't... personally agree with. If there's better reasoning for it though, I would not mind hearing it. Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #21 20121112 12:15:32
Re: Continuous FunctionsActually, I just realized I was looking at it differently. This in my opinion is another futile argument, I understand why it's a rule now. No need to further explain to me. I also understand the 2 = 1 proof now and see the error, I was having a...similar kind of issue with it. So with all my questions answered, I go back to with what I was originally going to say, but didn't say it quite clearly. I think the continuous functions page is very clear and well done. I didn't have an issue understanding it, only understanding indirectly relating things. Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #22 20121112 12:33:25
Re: Continuous FunctionsThanks Calligar. Questioning is an important part of mathematics. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #23 20121112 13:21:44
Re: Continuous FunctionsI'd agree, because I have high emphasis on myself for understanding things. It really bothers me if I walk away from something without understanding it well. It has also done nothing but help me with...well pretty much everything I know now (though there is still a lot I don't understand). So yeah, I will often question something I don't understand to better understand it. Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #24 20121112 20:40:35
Re: Continuous FunctionsHi MIF 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 20121113 07:33:35
Re: Continuous FunctionsSmooth function would need a page of its own, I think. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman 