Sentence examples for a strict inequality between from inspiring English sources

Also, a strict inequality between points may be defined as ({mathbf{v}} prec {mathbf{w}} ) if ({mathbf{v}} preceq {mathbf{w}} ) and ({mathbf{v}} neq {mathbf{w}} ).

Specifically, for v = ( v 1, v 2 ), w = ( w 1, w 2 ) ∈ R 2 we say that v ⪯ w if v 1 ≤ w 1 and w 2 ≤ v 2. Two points v, w ∈ R + 2 are said to be related if v ⪯ w or w ⪯ v. Also, a strict inequality between points may be defined as v ≺ w if v ⪯ w and v ≠ w.

In this subsection, we afford another stronger lower and upper solutions to get a strict inequality of the solution between them.

Hence (10) takes the form of a strict inequality.

It is easy to show that the above inequalities take the form of a strict inequality.

Hence (12) takes a strict inequality, so does (11), thus (14) is valid.

Hence, (7) takes the form of a strict inequality, so does (6), and we have (9).

The notation (prec ) will be used in this article to indicate a strict inequality.

If ϕ 1 = 1, then assume that (3.3) holds as a strict inequality.

Hence (2.5) takes a strict inequality and the same as (2.4), thus (3.2) is valid.

Moreover, the realizing matrix is (entrywise) positive if (1>lambda_{2}) and (3.3) is a strict inequality.