Is there a way to describe the set of all real points in a single equation with an equals sign? Instead, is it possible to create a "function" (I use function loosely as it mathematically is supposed to give only one output for an input.) which can be solved to equal all values which can be graphed?
I think it could've looked something like f(x) = x ∈ R, but first, set notation doesn't work in the graphing programs I'm using, (Desmos or Grapher for OSX) and second, saying that a variable is within the set of reals isn't very useful. Not only that but to use something like f(x) = R won't work without better defining the set of all reals, so I end up back at the beginning of my question.
the set of all points x such that x in reals and x-x=0, this doesn't get rid of the x in reals part. you can't because in general if something is true for the reals then it's true for the complexes. perhaps something like the set {x,y} such that (x)^2 = y has exactly two solutions but even this doesn't solve the problem because in the mod 3 field x^2=1 has exactly two solutions.