# Functions (math question) **URL:** \ **Category:** Factual Questions\ **Created:** [December 3, 2008, 1:59pm UTC](https://boards.straightdope.com/t/functions-math-question/475504 "2008-12-03T13:59:38Z")\ **Posts on this page:** 9\ **Page:** 3
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [December 4, 2008, 6:46pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/41 "2008-12-04T18:46:30Z")
> [@ultrafilter](#): > > There is a standard symbol for definitions, although I can’t reproduce it here. We should use that rather than a standard equals sign in function definitions for clarity. Are you referring to this? _f_(_x_) ≡ 4_x_[sup]2[/sup]-6_x_ (I can’t promise it shows up okay in other browsers. Three horizontal lines instead of two (=).) ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [December 4, 2008, 7:08pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/42 "2008-12-04T19:08:17Z")
> [@Pasta](#): > > Are you referring to this? > > _f_(_x_) ≡ 4_x_[sup]2[/sup]-6_x_ > > (I can’t promise it shows up okay in other browsers. Three horizontal lines instead of two (=).) No, that seems to have a slightly different connotation. I would write _f_(_x_) ≡ 0 to indicate that _f_(_x_) is equal to 0 for any _x_, no matter how _f_ is defined. The symbol I have in mind is given by riangleq in Latex, although I’ve also seen the word “def” over an equals sign. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [December 4, 2008, 7:28pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/43 "2008-12-04T19:28:07Z")
I see. I asked because ≡ didn’t seem quite right to me, either, but I couldn’t think of what else you would be talking about. I see now that it’s because I haven’t come across riangleq before. [image of rangleq](http://upload.wikimedia.org/math/d/9/1/d91c703bf2182f82d41f6976852ef4ad.png) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 4, 2008, 7:49pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/44 "2008-12-04T19:49:51Z")
Quoth **Tyrrell McAllister** : > [@](#): > > (2) I defined the function f using the equation f(x, y) = x[sup]2[/sup] + y[sup]3[/sup] x - 1. But the function f itself is not the equation. The equation was just one of the sentences I used to describe which function I was talking about. Some further elaboration on this: I might also define a function g such that g(v,w) = v[sup]2[/sup] + w[sup]3[/sup] v - 1. Having then defined both f and g, I can then say things like f = g. Note that this isn’t an equation of two _numbers_: I’m saying that the functions themselves are equal. Note also that I didn’t need any x or y in my equation of functions, or even in the definition of g: The x and y are just inputs to the function, not part of the function itself. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 4, 2008, 8:42pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/45 "2008-12-04T20:42:47Z")
> [@ultrafilter](#): > > No, that seems to have a slightly different connotation. I would write _f_(_x_) ≡ 0 to indicate that _f_(_x_) is equal to 0 for any _x_, no matter how _f_ is defined. The symbol I have in mind is given by riangleq in Latex, although I’ve also seen the word “def” over an equals sign. I’d never thought about it before, but I suppose the triangle in riangleq is supposed to be a delta, standing for “def[inition]”. But quick Googling is unable to confirm this, raising within me a fiery passion for a site devoted to the etymological history of mathematical notation. Which will no doubt subside into minor curiosity in a couple hours and be forgotten by tomorrow… ---
**Author:** ![sunacres](https://avatars.discourse-cdn.com/v4/letter/s/4491bb/32.png) [@sunacres](https://boards.straightdope.com/u/sunacres)\ **Post date:** [December 6, 2008, 8:28am UTC](https://boards.straightdope.com/t/functions-math-question/475504/46 "2008-12-06T08:28:00Z")
At the risk of compounding \*\*Hari Seldon’s \*\*cringe, I would like to express my appreciation to **RachelChristine** for initiating this thread and to the contributors for the ensuing discussion. I’ve just started teaching high school math and have three sections of freshman Algebra 1. I’m a mid-life career changer, having been an architect, civil engineer and software development manager in past lives. The whole point of this latest enterprise for me is to figure out how to communicate concepts effectively, and how to build in a child’s mind a working mechanism for absorbing, appreciating, and possibly for applying new ideas. I am shocked at today’s Algebra textbooks - they do not even aim at answering the kind of question that **RachelChristine** poses. The focus is now on skill development, in pursuit of proficiency in state-mandated standards. But that’s another thread. Every single day I experience a profound sense of awe at how transparent my own understanding of things is to me - tiny conceptions that seem completely self-evident but that are utterly outside of the experience of my students. Reconstructing the pathways to comprehension is sometimes an elusive task, but the challenge is so fascinating that I get up early and eager every morning. It’s also why I enjoy reading the Dope. Thanks folks. ---
**Author:** ![Digital\_Stimulus](https://avatars.discourse-cdn.com/v4/letter/d/aeb1de/32.png) [@Digital\_Stimulus](https://boards.straightdope.com/u/Digital_Stimulus)\ **Post date:** [December 6, 2008, 5:29pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/47 "2008-12-06T17:29:14Z")
> [@Napier](#): > > There is also the idea of pure functions, which I sort of grasp while I am reading about it, and the lambda calculus, and places it appears like in the computer language Scheme. > > Moreover, functions can be arguments to other functions, and so there are functions that operate on functions… Mmmm…[curry](http://en.wikipedia.org/wiki/Currying). ---
**Author:** ![Capt.Ridley\_s\_Shooting\_Party](https://avatars.discourse-cdn.com/v4/letter/c/cc9497/32.png) [@Capt.Ridley\_s\_Shooting\_Party](https://boards.straightdope.com/u/Capt.Ridley_s_Shooting_Party)\ **Post date:** [December 6, 2008, 6:42pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/48 "2008-12-06T18:42:32Z")
> [@Indistinguishable](#): > > I’d never thought about it before, but I suppose the triangle in riangleq is supposed to be a delta, standing for “def[inition]”. > > But quick Googling is unable to confirm this, raising within me a fiery passion for a site devoted to the etymological history of mathematical notation. Which will no doubt subside into minor curiosity in a couple hours and be forgotten by tomorrow… [Here’s](http://jeff560.tripod.com/mathsym.html) one, but it doesn’t have the riangleq symbol, unfortunately. It does note that the equality sign with “def” above it dates from Burali-Fority, 1894 (bottom of the set theory and logic section), though. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 6, 2008, 9:57pm UTC](https://boards.straightdope.com/t/functions-math-question/475504/49 "2008-12-06T21:57:57Z")
Oh, nice. Thanks for the site. [Previous page](https://boards.straightdope.com/t/functions-math-question/475504.md?page=2)