I am looking for a mathematical concept or model where functions like f(x) = 0*f(x-1) can be interpreted without defining a base case. In computer science, the function f(x) = 0*f(x-1) can sometimes be interpreted as 0, since 0*x = 0 thanks to “lazy evaluation”. But I am looking for a purely mathematical framework where this exact function is allowed and successfully returns 0.

I stumbled across mathematical concepts like corecursion, hypersets and not well-founded functions in my research, but I can’t find a clear statement that f(x) = 0*f(x-1) is really 0 in the context of hypersets. I guess this is because there is not that much literature about hypersets so it is hard to find out for me if the function returns 0.