That is diametrically opposed to something.
That contradicts something, such as an argument.
That is itself a contradiction.
Mutually exclusive.
Tending to contradict or oppose, contrarious.
Either of a pair of propositions, that cannot both be true or both be false.
Not similar or congruent; not matching or fitting in.
Of two numbers, with respect to a third, such that their difference can not be divided by it without a remainder.