Sentence examples for for every finite from inspiring English sources

This asserts that for every finite, two-person zero-sum game, there is a rational outcome in the sense that two perfectly logical adversaries can arrive at a mutual choice of game strategies, confident that they could not expect to do better by choosing another strategy.

for every finite sequence,.

Theorem 4.1 holds for every finite interval,,, and, when.

On the other hand, for every finite IFS, with contraction constant less then, we have.

A set-valued map is called KKM map if for every finite subset of (2.4).

Thus, if this alternative theory were true, it would mean God would have to create an infinite set of ideas for every finite mind.

For every finite-dimensional subspace W n ⊂ X, dim ( W n ) = n, there exists R n > 0 such that ∀ u ∈ W n : ∥ u ∥ = R n ⇒ E ( u ) ≤ E ( 0 ).

First of all, for every finite-dimensional space F ⊂ L { F j } and every v ∈ L { F j }, the function a ˜ ( F, v ) : F × [ 0, 1 ] → R, defined by a ˜ ( F, v ) ( x, s ) = 〈 A s x, v 〉, is continuous on F × [ 0, 1 ] because the operators T t and J are continuous and C satisfies the condition (c2).

There exist ρ > 0, α > E ( 0 ), and a subspace V ⊂ X of finite codimension such that ∀ u ∈ V : ∥ u ∥ = ρ ⇒ E ( u ) ≥ α. (2) For every finite-dimensional subspace W n ⊂ X, dim ( W n ) = n, there exists R n > 0 such that ∀ u ∈ W n : ∥ u ∥ = R n ⇒ E ( u ) ≤ E ( 0 ).  .

Assume, in addition, that: (1) there exist (rho>0), (alpha>f(0)) and a subspace (Vsubset X) of finite codimension such that forall uin Vmbox quad Vert u Vert =rhoquad Rightarrowquad f u) geq alpha;   (2) for every finite-dimensional subspace (Wsubset E), there exists (R>0) such that forall uin Wmboxquad Vert u Vert =Rquad Rightarrow quad f u) leq f(0).

A norm ideal C is said to satisfy condition (QK) if there exist constants 0for every finite-rank operator X and every k∈N, where X[k] denotes the direct sum of k copies of X.