Sentence examples for hence infinite from inspiring English sources

(1) After finitely many steps we get a group (G_i) which is hereditary just-infinite and elementary amenable, and hence infinite cyclic or (D_{infty }) (Theorem 4.5).

They are a class of normal logic programs whose consequences under the stable model semantics can be effectively computed, despite the fact that finitary programs admit function symbols (hence infinite domains) and recursion.

The results show that for a relatively low load, corresponding to 10% of the maximum supported by the joint, the number of cycles surpasses 1 × 106, hence infinite life of the service component can be attributed.

The reason of this exclusion is that the denominator in the normalized (C_{text{sm}}^) (defined later) becomes zero (hence infinite (C_{text{sm}}^)) which leads to 'ineffective' statistical data.

Under suitable conditions, an equation F x)=y between Banach spaces involving a nonlinear Fredholm mapping F of nonnegative index is shown to have a noncompact and hence infinite set of solutions for almost every y for which the equation is solvable.

But this contradicts the splitting lemma as for infinitely many (i) the quotients (G_i/G_{i+1}) are isomorphic to (mathbb Z ^{d_i}.) This proves the conjecture (C(1/2).) After finitely many steps we get a group (G_i) which is hereditary just-infinite and elementary amenable, and hence infinite cyclic or (D_{infty }) (Theorem 4.5).

Hence this infinite fraternity of feeling".

Some thought that GPs now had the keys to the NHS budget and hence had infinite access to resources enabling us to refer patients anywhere for anything.

Hence, an infinite discrete time resolution is achieved, enabling all MPCs to be resolved.

Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of 'hidden' variables.

The graph contains strongly connected components (SSC) equal to the state space nodes, implying that the model does not have any SSC with more than one node, and hence no infinite occurrence sequences.