Correct. In the extreme case, imagine that your k hash functions are nearly identical: hash function `H_i` differs from `H_1` only in that the outputs for the

Correct. In the extreme case, imagine that your k hash functions are nearly identical: hash function `H_i` differs from `H_1` only in that the outputs for the `1`st and `i`th elements in the input space are swapped. Of the `N` elements in the input space, all but `k` will completely collide.