Question

I understand that hardware will limit the amount of memory allocated during program execution. However, my question is without regard to hardware. Assuming that there was no limit to the amount of memory, would there be no limit to the array?

Answer 1

There is no fixed limit to the size of an array in C.

The size of any single object, including of any array object, is limited by SIZE_MAX, the maximum value of type size_t, which is the result of the sizeof operator. (It’s not entirely clear whether the C standard permits objects larger than SIZE_MAX bytes, but in practice such objects are not supported; see footnote.) Since SIZE_MAX is determined by the implementation, and cannot be modified by any program, that imposes an upper bound of SIZE_MAX bytes for any single object. (That’s an upper bound, not a least upper bound; implementations may, and typically do, impose smaller limits.)

The width of the type void*, a generic pointer type, imposes an upper bound on the total size of all objects in an executing program (which may be larger than the maximum size of a single object).

The C standard imposes lower bounds, but not upper bounds, on these fixed sizes. No conforming C implementation can support infinite-sized objects, but it can in principle support objects of any finite size. Upper bounds are imposed by individual C implementations, by the environments in which they operate, and by physics, not by the language.

For example, a conforming implementation could have SIZE_MAX equal to 2¹⁰²⁴-1, which means it could in principle have objects up to 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137215 bytes.

Good luck finding hardware that actually supports such objects.

Footnote: There is no explicit rule that no object can be bigger than SIZE_MAX bytes. You couldn’t usefully apply the sizeof operator to such an object, but like any other operator, sizeof can overflow; that doesn’t mean you couldn’t perform operations on such an object. But in practice, any sane implementation will make size_t big enough to represent the size of any object it supports.