It's named for sizeof, a C operator which returns a positive integer but annoyingly the core C language itself doesn't define what the type of that integer is, the standard library does though, naming it size_t
Now, sizeof does measure the size of things, but, one of the obvious sizes you can measure is an array†, and that's definitely also the maximum index value for the array, so I do think it's fair to say that's (part of) literally why size_t exists.
† One of C's treacherous footguns. In the scope where the array was defined it's an array, and sizeof(array) tells you how big that array is. But, passed as a parameter it becomes a pointer and sizeof(resulting_pointer) is the size of the pointer, not the array :(
>Now, sizeof does measure the size of things, but, one of the obvious sizes you can measure is an array†, and that's definitely also the maximum index value for the array
Make sure to be careful and realize that sizeof my_array returns the number of bytes that my_array uses, not the number of elements. An array of 10 ints likely has sizeof == 40, while indexing past 9 would be undefined behavior.
Excellent point, that largely contradicts my earlier position in fact. I was thinking of an array of chars and should have considered that's only a special case.
The core language says that the result of sizeof is size_t, defined in <stddef.h> (and other headers).
size_t is a typedef (alias) for an implementation-defined unsigned integer type.
It could have been worded differently with the same meaning. For example, the core language (section 6 of the standard) could have said that sizeof yields a result of an implementation-defined unsigned integer type without referring to "size_t". The library section (section 7) already says that size_t "is the unsigned integer type of the result of the sizeof operator". Personally I think that referring to size_t in the language section adds clarity, even if it's slightly redundant.
In a given implementation, a compiler might arrange for sizeof to yield a result of type unsigned long, for example. The corresponding <stddef.h> header must then define size_t as unsigned long for the implementation to be correct.
Now, sizeof does measure the size of things, but, one of the obvious sizes you can measure is an array†, and that's definitely also the maximum index value for the array, so I do think it's fair to say that's (part of) literally why size_t exists.
† One of C's treacherous footguns. In the scope where the array was defined it's an array, and sizeof(array) tells you how big that array is. But, passed as a parameter it becomes a pointer and sizeof(resulting_pointer) is the size of the pointer, not the array :(