Even that is not infinite because there is a limit to how much memory you can address. You don't have to bring physical realities into it.
Really, the crux of the matter is that you can have a function call itself an unbounded number of times in C (i.e. unbounded recursion). That you eventually run into a stack overflow is a limitation of the machine, not of the language; the definition of C does not prescribe a maximum number of recursive calls. This, together with conditionals, makes the C language Turing-complete.