Sentence examples for namely such that from inspiring English sources

Fix a compatible set of primitive mth roots of unity (xi _m,) namely such that (xi _{me} ^e = xi _m ) for all (e > 0).

By Lemma 2.10, there exists a subset of finite logarithmic measure, namely such that for some point satisfying and, we obtain (5.13).

We fix a compatible set of primitive m –th roots of unity ξ m, namely such that ξ m e e = ξ m for all e > 0. Let R = R n and R ~ = R n, m.

Even granting that there is an operator, say, *, which behaves as dialetheists claim (namely, such that in particular in some cases A is true together with *A), it is still perfectly possible to define a Boolean negation with all the properties of classical negation (in particular, the property of being explosive).

Since (Gamma ) is finitely presented, there exists a finite subset (R subset F_ell ) of words (v_1, ldots, v_m) in the letters of (U cup U^{-1}) such that (ker (q)) is the normal subgroup of (F_ell ) generated by (R), namely such that (langle U mid R rangle ) is a presentation of (Gamma ).

By (H.5), we can prove that since the numerator of is an decreasing function of b, and the denominator of is always positive, then if we decrease a real time user's utility function parameter from to 0, then there always exists a value for parameter, namely,, such that and when then, therefore, when there is no such.

Assume that f satisfies the uniformly Lipschitz condition, namely there exists (L>0) such that biglVert f t,z_{1})ominus_{g}f(t,z_{2}) bigrVert _{I}leq L|z_{1}ominus_{g}z_{2} |_{I}, (6.14) with (forall tin J) and (|z_{1}|_{I}, |z_{2}|_{I}leq M_{alpha}).

Namely, there exists a constant such that (4.21).

Namely, if is given then find such that implies.

Hence, since by (6) Fm/θ(T) ∈ K, it follows that if Γ ⊬L φ, then there is an algebra A (namely Fm/θ(T)) and a valuation v (namely id) such that the elements of v satisfy the equation on A but v does not.

To identify the value of and, we consider every possible division of network locations into two subsets, namely, and, such that and.