A pointer is just a number

He's wrong. A pointer, at least in C, is not a number, and saying that it is just causes confusion.

Pointers have some of the same properties as numbers (specifically integers). In particular, you can do arithmetic on them -- but only in a very restricted way. You can add or subtract an integer to a pointer, yielding a pointer, and you can subtract a pointer from a pointer, yielding an integer.

Most current architectures have a single monolithic addressing space, and pointers can be treated as indices into that address space, treated as a very large array. But the C standard is carefully written to permit other memory models.

For example, pointers to distinct objects cannot meaningfully be subtracted or compared, except for equality or inequality.

Sure, a pointer is represented as a sequence of bits, and that sequence of bits can be treated as an integer -- but the mapping is unspecified. Similarly, a floating-point representation can be mapped onto an integer representation; that doesn't mean that the integer value 1069547520 will help you understand the floating-point number 1.5.

A pointer is a pointer. If you want to understand how pointers work, learn about pointers.

See also sections 4 and 6 of the comp.lang.c FAQ at http://www.c-faq.com/.

A function is a type, is a set, is a number. And that, frankly, is difficult to get around. Coming from the C / Java world, it is hard to understand that "types" are really sets (in a mathematical sense) which in turn, are numbers (i.e. the set of natural integers), and a function (in terms of the value it returns) is a number as well and can be considered as being an "operation" upon a set, i.e., put set A into set B and one has set C. Function == Type == Set == Number, or, perhaps, a Number is simply an instance of a Set which in turn is another way of saying Type, so, basically, Function == Set. What makes it conceptually difficult is that the word "function" entails "operation", which entails "time", when, really, one could think of "function" as sort of being "those steps one has to go through in order to define a set of type S".

A set is a theorem, so now we have, Theorum == Type == Set == Number. A function is simply the way of defining or proving the Theorum, e.g. if set A == B, and B == C, then A == C is a function, which itself is a Set, conjoining A and C.

The "type" of an object (integer, char, whatever) is really a Set, and the way to construct that set (also being itself a set) is a function, which is what one might call a "program".

These things are different ways of looking at the same thing. A "type" (set) is the Theorum, its proof is the function (program which constructs the Theorum or Set).

The only difference between function/program and Set/Theorum is the former "constructs" the later, the former being "temporal" the latter being "eternal" or put it another way, the former being the "building blocks" the latter being the "finished product".

So yes pointers are numbers, which though are Sets, constructed by functions and these sets construct the Theorums. The type is the Theorum, the function is the construction of that Theorum, done vis-a-vis Sets and that is what (IMHO) that thing which we call "computer science" is all about. :-)

A good thought, but C’s syntax makes it a bit hairy to explicate that you’re using an integral value as a pointer:

    #include <stdint.h>
    #include <stdio.h>

    struct big_data { int i; };

    void f(intptr_t p) {
        printf("%d\n", ((struct big_data*)p)->i);
    }

    int main(int argc, char** argv) {
        struct big_data data = { 42 };
        intptr_t p = &data;
        f(p);
        return 0;
    }

So there’s no real pedagogical gain. If someone understands what “a pointer is just an integer” means, then they probably understand pointers already.

I've always found it helpful to explain a pointer as exactly that - a pointer, ie. a person standing there pointing at something.

If you need to keep track of something and know that no matter where you put him he's always going to be pointing at the same thing, sometimes it's going to be easier to move him around than, say, the 72-story building he's pointing at.

If you need to explain it more technically then the simple truth of them tracking the memory address of something has always seemed the best approach - then start learning what that actually means if need be. Anyone hoping to end up using C for much and not be shooting yourself in the foot constantly should be learning at least the basics of such things anyway.

Coming from Java, I didn't understand the point of pointers (no pun intended) until I was re-reading through chapter 1 of K&R C.

At one point, they mention how when you pass a variable into a function, it only passes the value really, "copying" the variable, in a way. Then they go on to say that changing the original variable is talked about in chapter 5, which covers pointers. Then it just clicked. If you want to change the original value, pass a pointer to said variable. If you want to just use the value of a variable, pass the variable through the function.

It's so much easier than what I was doing before, assigning the variable to the return value of a function.

Er... yes? But I suppose every piece of data on a computer could be considered a number as well.