That is not entirely true. If you compare two implementations of bubble sort, they will both be O(n^2). Yet one can still be much more efficient than the other.
x^4 and x^10 are both polynomials.
x^4 and x^10 are both polynomials.
what are you referring to?
Obviously x^4 != x^10, but noone has ever proven that "if SAT is P, then it would have the lowest (or highest) polynomial complexity among the other problems", or anything similar
> [All NP-hard problems] have equivalent difficulty.
I get what OP meant, but there can still be some NP-hard problems that are more difficult than others.
As I said, x^4 and x^10 are both polynomials. I wouldn‘t call them "equivalent" though.