Sentence examples for trivial elements from inspiring English sources

This extension sends elements of P3 to trivial elements of C 3 ′ Open image in new window, so induces a morphism ϕ : C 3 → C 3 ′ Open image in new window satisfying the conditions to make (ϕ,I d,Id) a morphism of quasi 3-crossed modules.

The scene you describe is but a trivial element of the society, missing the real substance of Miami Beach's beautiful lifestyle.

The trivial element in S 4 will be denoted as e.

If f is quasiconvex, then for all (uin Xsetminusargmin_{X}f), the set (N_{f}^{a} u)) has non-trivial elements.

Stable homotopy groups of spheres are used to describe the group Θn of h-cobordism classes of oriented homotopy n-spheres (for n ≠ 4, this is the group of smooth structures on n-spheres, up to orientation-preserving diffeomorphism; the non-trivial elements of this group are represented by exotic spheres).

The order of each non-trivial element of D8/Z(D8) is 2, so D8/Z(D8)≅V4; hence, I n n(D8)≅V4.

The non-trivial element of (mathbb {Z}_2) is represented by a sign change, (R_0 rightarrow - R_0) and (R_1 rightarrow - R_1,).

The left action is not free in general, since it is possible to have (g(xv =xv) for all (vin X^*) and for a non-trivial element (gin G), which will imply, by definition of the left action, that (gcdot x=x).

The shot should run for the entire length of the song; instead, the producers intercut Holiday's performance with shots of other actors and superimpose trivial expositional elements over her face.

On the other hand, the consistency of an atomistic theory is typically guaranteed by the trivial one-element model (with 'P' interpreted as identity), though one can also have models of atomistic theories that allow for infinite domains.

By the universal property of (U mathfrak {l})), this is the same as to say that the (U mathfrak {l})) has an ideal of finite codimension which contains no non-trivial primitive elements.