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

You are not logged in. #26 20120722 13:23:47
Re: 0^0 equals 1 or undefined?Yes. I see nothing wrong with that equality even if x=0. It's the step 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. #27 20120722 13:49:09
Re: 0^0 equals 1 or undefined?Yes, it is applying that identity, which should be true for all x,a and b. But because this leads to division by zero, we rather leave 0^0 as undefined. 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 #28 20120722 14:38:22
Re: 0^0 equals 1 or undefined?Yes. I agree that x^0 = x^(11) even if x=0. It's the x^(11) = x^1 * x^(1) I have trouble with. Last edited by noelevans (20120723 10:08:43) 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. #29 20120722 14:45:27
Re: 0^0 equals 1 or undefined?It leads to an undetermined expression for x=0 so that means the starting expression is also undetermined for x=0. 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 #30 20120723 09:10:51
Re: 0^0 equals 1 or undefined?
Also, http://mathworld.wolfram.com/ExponentLaws.html
But by my argument (post #21), 0^0 can be defined to be either 0 or 1. If it was undefined, then we couldn't add integers!
because what about , which never goes through the origin. And if you graph , it has strange behavior not just at the origin.#31 20120723 10:47:13
Re: 0^0 equals 1 or undefined?0/0 is symbolism in calculus for an indeterminate form, not for a number in the Reals. 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. #32 20120723 21:53:29
Re: 0^0 equals 1 or undefined?My argument from the other topic, Don Blazys', applies here, too. If we remove the removable singularity, we won't get the same 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 #34 20121215 21:58:52
Re: 0^0 equals 1 or undefined?There is no reason to put that into hide tags... 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 #35 20130127 03:53:42
Re: 0^0 equals 1 or undefined?I consider 0 infinity, because it is beyond definition and 0^0 is the same.  n872yt3r Math Is Fun Rocks! By the power of the exponent, I square and cube you! #36 20130127 14:01:46
Re: 0^0 equals 1 or undefined?The best exaplnation is right here 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. #37 20130207 20:23:13
Re: 0^0 equals 1 or undefined?The "cleverest" student is also erring, because, just because the limit is 1 at that point, doesn't mean that the value of that function at that point 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 #38 20130207 20:26:10
Re: 0^0 equals 1 or undefined?I have to disagree, it is not undefined. It is defined as 1 for convenience. 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. #39 20130207 20:32:03
Re: 0^0 equals 1 or undefined?Who says so? 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 20130207 20:35:42
Re: 0^0 equals 1 or undefined?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. #41 20130207 20:38:03
Re: 0^0 equals 1 or undefined?Hi Stefy
Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #42 20130207 20:51:04
Re: 0^0 equals 1 or undefined?Hm, okay then. But what are the privileges of defining 0.999... to "exist" as a mathematical concept and be equal to 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 #43 20130207 20:54:34
Re: 0^0 equals 1 or undefined?For one thing we would have to replace the geometric sum with some other answer. Pretty messy! 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. #44 20130207 20:58:22
Re: 0^0 equals 1 or undefined?Like what? 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 20130207 21:04:39
Re: 0^0 equals 1 or undefined?Hi; Hint 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. #46 20130207 21:12:59
Re: 0^0 equals 1 or undefined?Last edited by anonimnystefy (20130207 21:14:13) 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 20130207 21:16:45
Re: 0^0 equals 1 or undefined?Yes, so we would have do away with this: Want to see a reason why we need 0^0 = 1? 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. #48 20130207 21:20:13
Re: 0^0 equals 1 or undefined?No, the 0^0 is okay. 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 #49 20130207 21:22:11
Re: 0^0 equals 1 or undefined?You did not understand. Which you have already said was 1 because of the sum of a geometric series. 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. #50 20130207 21:25:05
Re: 0^0 equals 1 or undefined?No, that sum 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 