Creating clues to a safe

The list of clues can be "1) The code is not $0000$ , 2) the code is not $0001$ , 3) the code is not $0002$ " and so on, skipping over the actual code itself.

As there are $10^4 = 10000$ four digit combination codes, the logician would be required to have all $10000 - 1 = \boxed{9999}$ clues to deduce the missing one.

Any clue list with $10000$ clues or more must have a redundant clue, so this is the longest list of clues that can be created.

9999 was my initial answer. But on 2nd thought, I think it's 0.

The clue list doesn't have to be in the form of "it's not 0000, it's not 0001 ... ". E.g., it can be a list of eqn's like this one: Let X1 (the code), X2, ..., Xn be n unknowns, & c(1,1), ... c(jk), ..., & A1, .. An are known constants. I can write sth like:

c(1,1)•X1 + c(1,2)•X2 + ... + c(1,k)•Xk = A1
c(2,1)•X1 + c(2,2)•X2 + ... + c(2,k)•Xk + c(2,k+1)•Xk+1 = A2
c(3,1)•X1 + c(3,2)•X2 + ... + c(3,k)•Xk + c(3,k+1)•Xk+1 + c(3,k+2)•Xk+2 = A3
......
c(n,1)•X1 + c(n,2)•X2 + ... + c(n,k)•Xk + c(n,k+1)•Xk+1 + c(n,k+2)•Xk+2 + ... + c(n,n)•Xn = An
...

Solving n eqn's w/ n unknowns reveals the code X1. When n -> ∞, w/ each eqn being a clue, the clue list can be arbitrarily long. This is just one e.g. It's obvious that there're also infinite no. of ways to formulate these arbitrarily long clue lists.