Sentence examples for exist infinitely from inspiring English sources

One might, perhaps, think that the mere existence of many-valued logics shows that there exist infinitely, in fact, uncountably many truth values.

We show that if energy gap occurs, then there exist infinitely many weakly harmonic maps for the Dirichlet problem under some topological assumptions of the target manifold.

As direct corollaries, it implies the generalized Yau's conjecture for such manifolds with positive Ricci curvature, which says that there exist infinitely many pairwise non-isometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves.

In this paper, we prove that on every Finsler 2-dimensional sphere, either there exist infinitely many prime closed geodesics or there exist at least two irrationally elliptic prime closed geodesics.

There exist infinitely many dishonest processes with this Q-matrix.

For our mathematical theories entail that there actually exist infinitely many different mathematical objects.

If x 0 is not a strict local minimizer of J, then there exists infinitely many critical points near x 0 and the conclusion holds.

Hence, if the conditions of these existence results do not hold for some repeated games, there still may exist an infinitely split Nash equilibrium.

There exists an infinitely differentiable function defined on with values in, which cannot be represented as any superposition constructed from several infinitely differentiable functions defined on with values in.

If H also satisfies H −t,q,−p)="H t,q,p) for any (t,q,p ∈R×T∗M, it is shown that the time-1-map of the Hamiltonian system (if exists) has infinitely many periodic points siting in the zero section of T∗M.

What happens is that below Tc there exists an infinitely degenerate set of ground states, in each of which the spins are all aligned in a given direction.