[dbaupp]

What exactly are you nitpicking?

1000^depth is not a constant: the function here is "f(depth) = number of times the inner loop body executes". f(depth) = O(1000^depth).

And, "times" here is serving the same role as "comparisons" in "Mergesort takes O(n log n) comparisons": it's referring to the thing that f is actually counting.

[colanderman]

Given O(f(x)), x is almost always understood to be measurement of the work input to the algorithm. Loop nesting depth is not a measurement of work input, it's a property of the code – "1000^depth" is constant for any given algorithm.

Yes, O(…) is just a mathematical construct, so you can apply it the way you have to mean "the amount of work done for a given input size increases exponentially with respect to the number of nested loops iterating over the input"… but that's not how most people interpret it in the context of a computer algorithm. (The exception would be if the nesting depth were dynamically determined by an input parameter, but I don't think that's what anyone here is talking about.)

Anyway I'm not trying to argue, I agree with your point, but I think everyone here is talking past each other trying to say the same thing, ultimately due to imprecision in semantics.

[dbaupp]

The only difference between what is "code" and what is "work" is context: in this case, the work of interest is a property of some input code. If you want a framing that matches your notions of input better, just imagine we're measuring the asymptotics of a VM/interpreter, and then the code truly is the input.