Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a name for a position on a function surface and the value at that position? E.g., if I have the function $f(x,y) = x^2 + y^2$, and I know that at the point $(2, 2)$ it evaluates to $8$, is there a name for the data structure $(2, 2, 8)$ [which is in this example $(x, y, f(x, y))$]?

share|cite|improve this question
This doesn't quite answer your question, but the set of all points of the form $(x,y,f(x,y))$ is called the graph of the function $f$, so in your case, $(2,2,8)$ is a point in the graph. In general, for any function $f : X \to Y$ between two sets, the set $\{ (x,f(x)) \mid x \in X \} \subseteq X \times Y$ is the graph of $f$. – fuglede Oct 5 '11 at 20:36
up vote 2 down vote accepted

It is an element of the graph of $f$. The formal definition of the graph of a function $f:X\to Y$, where $X$ and $Y$ are any two sets, is the subset $\Gamma(f)\subset X\times Y$ consisting of $$\Gamma(f)=\{(x,y)\in X\times Y\mid y=f(x)\}.$$ So, in your case, $X=\mathbb{R}^2$ is the plane, $Y=\mathbb{R}$ is the real numbers, and $$\Gamma(f)=\{((x,y),z)\in \mathbb{R}^2\times \mathbb{R}\mid z=f(x,y)\}.$$ But we usually identify $\mathbb{R}^2\times\mathbb{R}$ with $\mathbb{R}^3$, of course, and we get $$\Gamma(f)=\{(x,y,z)\in \mathbb{R}^3\mid z=f(x,y)\},$$ or in other words, $\Gamma(f)$ consists of the triples $(x,y,f(x,y))$, such as $(2,2,8)$.

share|cite|improve this answer
Thanks. I am guessing there is no fancy name for "element of the graph of f"? – shino Oct 5 '11 at 21:24
No, I don't believe so. – Zev Chonoles Oct 6 '11 at 2:06

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.