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You are not logged in. #1 20121104 09:29:42
'Gap' in Graph of x^y = y^xI was looking at the graph of x^y = y^x today and I was curious about the point where the two lines meet (you'll know what I mean if you look at the graph). Initially I guessed that that might be the point (x,y) = (e,e) but according to WA it seems like a range of values for which this function is discontinuous. What is this range of values, and why is this the case? #2 20121104 10:30:00
Re: 'Gap' in Graph of x^y = y^xThat isn't even a function, let alone a continuous one... 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 #3 20121104 10:32:20
Re: 'Gap' in Graph of x^y = y^xIs that a proper function? 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 #5 20121104 10:34:37
Re: 'Gap' in Graph of x^y = y^xA function has exactly one value of y for any given x in the domain of the function. 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 20121104 10:35:21
Re: 'Gap' in Graph of x^y = y^xY can only have one value. 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 #7 20121104 10:40:41
Re: 'Gap' in Graph of x^y = y^xOh I see, so y^2 = 4ax are also not functions, then? I did think that functions had to be onetoone, but that sort of graph (or something like (x^2  2)^2 + (y^2  2)^2 = 2) is manytoone. #8 20121104 10:42:35
Re: 'Gap' in Graph of x^y = y^xNo, it is a function. 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 #9 20121104 10:43:05
Re: 'Gap' in Graph of x^y = y^xIt doesn't have to be onetoone. 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 20121104 10:45:02
Re: 'Gap' in Graph of x^y = y^xy^2 = 4ax would be a parabola. 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 #11 20121104 10:46:13
Re: 'Gap' in Graph of x^y = y^x
Why? #12 20121104 10:48:53
Re: 'Gap' in Graph of x^y = y^xIs it not the form for a parabola? 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 #13 20121104 10:51:22
Re: 'Gap' in Graph of x^y = y^xYes, it is a parabola, but I'm not understanding why that would be a function (you can have two values for y given a value for x), but x^y = y^x is not a function, even though there are two values for y you can have given an xvalue. #14 20121104 10:53:15
Re: 'Gap' in Graph of x^y = y^xy^2=4ax is not a function. 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 #15 20121104 10:53:16
Re: 'Gap' in Graph of x^y = y^xWell, you would consider it as a function. For example: 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 #16 20121104 10:58:18
Re: 'Gap' in Graph of x^y = y^x
I know that y^2 = 4ax is the general form of a parabola, I was just asking why it was not a function... #17 20121104 10:59:46
Re: 'Gap' in Graph of x^y = y^x(0,1), (1,0), (2,0), (3,2) 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 #18 20121104 11:01:25
Re: 'Gap' in Graph of x^y = y^xy=x^2. At every value of x has only one value of y, but 1 and 1 yield the same value of y. 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 #19 20121104 11:02:31
Re: 'Gap' in Graph of x^y = y^xOh I see, so the distinction is that it can be many to one, but not one to many. #20 20121104 11:03:13
Re: 'Gap' in Graph of x^y = y^xIn those terms, yes. 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 #21 20121104 11:07:27
Re: 'Gap' in Graph of x^y = y^x
Yes. Another thing that must be satisfied by a function is that it must have a value at every element of its domain. 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 20121104 11:12:49
Re: 'Gap' in Graph of x^y = y^xZeta, if you don't mind me questioning, what course are you taking? 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 #24 20121104 19:44:41
Re: 'Gap' in Graph of x^y = y^xhi zetafunc You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 