Set of non-decreasing function in bijection with R I've learnt and understood the demonstration for "the set of all non-decreasing function is uncountable" with the diagonalization proof, but how could i demonstrate it is in bijection with R (the set of real numbers) or that the two sets are equipotent.

To identify a function it is enough to know its value on rational numbers and on the discontinuities. In fact the value on a continuity point $x$ is determined as the limit on rational points approaching $x$. A non-decreasing function has only a countable number of discontinuities, hence it is enough to know its value on a countable number of points.
