If you use the definition of a function as a set of ordered pairs which relate elements from two sets, how would this apply when you have a function of more than one variable, say 2?
Would the ordered pairs be of the form $((a,b),c)$?
Asked
Active
Viewed 47 times
2
-
Yesssssss....... But there is a natural one to one correspondence between $(X\times Y)\times Z$, that set of ordered pairs of an ordered pair and a unitary value, and $X \times Y \times Z$, the set of ordered triplets, that for our sake of sanity we consider an ordered pair of the form $((a,b),c)$ and an ordered triplet $(a,b,c)$ to be equivalent. Technically they are different. But practically they are not. – fleablood Sep 05 '18 at 16:02
1 Answers
2
A function with domain $X$ and codomain $Y$ can be identified with a set of ordered pairs $(x, y)$ with $x \in X$ and $y \in Y$, regardless of the structure of the underlying sets. If $X$ is a product, e.g. $X = A \times B \times C$ then each $x \in X$ is an ordered triplet, and so we have an ordered pair where the first element is (in turn) an ordered triplet).
So a three-variable function might look like a set of pairs of the form $\big((a, b, c), y\big)$.