I'm curious as to what the problem with infinities is.
Does a rational number not have an infinite expansion?
Does an algebraic number, too, noth ave an infinite expansion?
And why then would we not consider a trascendental number to be a valid entity, on the ground of it's infiniteness? It's the limit of an infinite sum, bounded between successive pairs of algebraic numbers, which themselves could too be considered an infinite sum.
