bo198214 Wrote:@Ivars: this proof also works for hyperreals.

Based on "language analogy" between real and hyperreal sets?

I will look into this deeper before making any new statements.

At least, as a first step, is it possible to construct such discontinuos function f(x) on real numbers which in each point is 0 if the point is approached from left, and 1 if approached from right( or vice versa)? So:

Alternatively :

Can we define a discontinuous function in such manner?

The one use of such function as a function of would be for any to discern from which side we are approaching it.

If we approach from left, this function has value e.g. 0 (alternatively 1)

if we approach from right ,this function has value e.g. 1 (alternatively 0)

Ivars