A mathematical expression that gives 0 if variable is different from constant and 1 if variable same as constant

Question

Example, ∆ = any mathematical expression; c = constant; x = variable;

c∆x=1 (if c = x) c∆x=0 (if c ≠ x)

am just asking?

Answer 1

You can use an Iverson bracket and write $[\Delta=c]$, though you should explain it the first time that you use it.

Answer 2

What you are describing is the Dirac delta function $\delta(x)$, which is often used in theoretical physics.

In your case, the function $\delta(x-c)$ has the property that it has value $1$ if $x=c$, and value $0$ if $x \neq c$.

For more details, you may wish to refer to this Wikipedia article: https://en.wikipedia.org/wiki/Dirac_delta_function