That sort of ambiguity is the reason for the strict inequality of the sampling theorem's condition.

König's theorem is remarkable because of the strict inequality in the conclusion.

In either case, a is not equal to b. These relations are known as strict inequalities.

Alternatively, the preceding terms are often defined requiring the strict inequality instead of in the foregoing definitions.

Shelah showed that it is consistent to have the strict inequality .

The strict inequality (9.2) is used to exclude the possibility of equality in (9.1) for every k.

If some but not all numbers are zero, we have strict inequality.

Therefore, it remains to prove strict inequality if they are not all equal, which we will assume in the following, too.

It remains to show strict inequality if not all x are equal.

(With at least one that gives a strict inequality)