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

You are not logged in. #1 20070622 13:21:34
What is a Function?I have been a bit adventurous and written a draft page on What is a Function?. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20070622 13:56:52
Re: What is a Function?
This is not correct, by normal standards. Square root is a function, this is why when solving equations we typically write something such as: We need the plus or minus in there because when we say "square root" we mean the positive root. It would be nice to mention that we define square root this way because we want it to be a function. If you want an example of something that isn't a function, sin¹ is not. It only becomes a function when the domain of sin is restricted to (pi, pi). A picture with the vertical line test would help as not many know what sin¹ looks like. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20070622 16:12:49
Re: What is a Function?So if there is no infront of the square root, it means it is positive?#4 20070622 16:20:11
Re: What is a Function?Correct. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20070622 17:39:19
Re: What is a Function?
Good idea. Plot looks like this: Plot of asin(x). "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #6 20070622 18:22:31
Re: What is a Function?
Square root is indeed a function for nonnegative real numbers. However, it is not a function for negative real numbers or complex numbers (since, for complex numbers in general, there is no positive or negative). For example, √(−1) = ±i. Last edited by JaneFairfax (20070622 18:36:16) #7 20070623 00:33:00
Re: What is a Function?Ah, true Jane. In that case, I would stick with square root and leave out sin¹, and say that the square root is a function over positive real numbers, but it isn't a function over all real numbers, using 1 as an example. I would also make sure to emphasize with this example that whether something is a function or not can depend on what set you use for the domain, and that you can use just about any set you want. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20070625 11:33:47
Re: What is a Function?Redid What is a Function? and Domain, Range and Codomain. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #9 20070627 18:33:23
Re: What is a Function?I can't seem to see the 'not single valued' image. It just shows as text. #10 20070627 19:00:00
Re: What is a Function?The image with the alt text “not single valued" seems to be missing. #11 20070627 20:15:19
Re: What is a Function?Ahh, thanks, fixed it. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #12 20070701 16:10:05
Re: What is a Function?Yes. Now that the problem is fixed, it may be added. Character is who you are when no one is looking. #13 20070701 16:33:16
Re: What is a Function?Thanks gman! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #14 20090914 13:55:43
Re: What is a Function?I have redone the What is a Function? page. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #15 20090914 17:08:10
Re: What is a Function?Hi MathsisFun; Last edited by bobbym (20090914 17:20:25) 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. #16 20090914 17:49:26
Re: What is a Function?Thanks! Will fix. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #17 20091008 15:41:05
Re: What is a Function?Well you wouldn't believe it, but I have been working on this page again. I wanted to make it clear that a function is a special type of relationship (a relationship may be valid but not a function). "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #18 20091008 18:54:57
Re: What is a Function?Hi MathsisFun;
I agree, your fundamentals determine your success. Last edited by bobbym (20091008 19:00:22) 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. 