Consider a simple linear function f(x)=ax. It maps the whole real axis bijectively to itself so long as “a” is not 0. However if a=0 everything collapses into t

Consider a simple linear function f(x)=ax. It maps the whole real axis bijectively to itself so long as “a” is not 0. However if a=0 everything collapses into the origin. The math that wraps some infinite process inside can be counterintuitive even as it makes things easier to compute. However it is not clear if the physical picture that involves singularity is real or just idealized approximation.