Is it possible to create a formula that is fulfilling following conditions, using only elementary functions/arithmetic?

Question

Conditions:

So $$f(X,L)=\begin{cases}-L&X=L\\0&\text X\ne L\end{cases}$$

Is it possible to construct a formula fulfilling these conditions using only elementary arithmetic/functions?

No, unless you count things like finding the maximum or finding the absolute value as elementary enough. — Ethan Bolker, Nov 26 '17 at 19:05
If these conditions have some property that makes it impossible, you could point it out and post it as an answer :) . — Łukasz Zaroda, Nov 26 '17 at 19:07
The answer with max/abs as "the best one can get" would be also great. — Łukasz Zaroda, Nov 26 '17 at 19:10
On second thought max and abs may not be enough since those functions are continuous and yours is not. — Ethan Bolker, Nov 26 '17 at 21:28

score 0 · Answer 1 · answered Nov 26 '17 at 19:24

0

How about $$-L\delta_{ (X, L)}$$ where $\delta$ is the Kronecker $\delta$ function?

Or if that is not elementary enough: $$-L\lim_{ t \to L} \frac {t-L}{t-X}$$

answered Nov 26 '17 at 19:24

Stephen Meskin

1 Answers1