Are all Equations Functions?

Question

Are all Equations Functions?

That is, does an Equation always imply a Function?

Thanks.

What do you mean? An equation is completely different from a function. — Peter Foreman, Apr 07 '19 at 13:34
Relations defined by some equality of the type $f(x, y) = 0 \iff x,\rho, y$ where function $f$ is given, aren't necessarily functions. — Jakobian, Apr 07 '19 at 13:37
See the post Transforming equations : equations are mathematical exprsssions using equality. They usually use functions, like $+, \times$. — Mauro ALLEGRANZA, Apr 07 '19 at 13:39

score 1 · Answer 1 · answered Apr 07 '19 at 13:37

No, an equation just states that two things are equal. If an equation can correspond to a mapping between variables, only then is it a function

For example, $\quad x=x,\quad1=1, \quad2+2=4\quad$ are all identities, i.e. equations that are always true, and are not functions.

But $y=x$,$\quad$ $x^2=y+z$ can all be interpreted as functions, as they show relationships between variables which can be used for mapping one variable to another.

Sweet, that made perfect sense. Thanks you aman. – Apr 07 '19 at 15:32 — , Apr 07 '19 at 15:32

Are all Equations Functions?

1 Answers1