Are you referring to this?
f(x) ≡ 4x[sup]2[/sup]-6x
(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.
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.
Quoth Tyrrell McAllister:
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.
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…
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.
Mmmm…curry.
Here’s 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.
Oh, nice. Thanks for the site.