Sentence examples for but we cannot deduce from inspiring English sources

But we cannot deduce that φ is true of all numbers, ∀xφ(x); this inference step requires the rule of mathematical induction: In other words, to prove that ∀xα(x) one proves that α(0) is the case, and that α(succ(n)) follows from the assumption that α(n).

For example by sorting the cells for their stem cell-like properties, the result is only a snapshot of the cells' state, but we cannot deduce from this observation that also the bulk cells cannot acquire such properties.

For example, the first intron of Tru1.5 is conserved in Tni1.2 but not Tru1.1, while the third intron of Tru1.5 is conserved in Tru1.1 but not Tni1.2, so we cannot deduce which intron was gained first.

Carboxylate peaks obscure any possible litharge detection in Figure 2 and SR-XRD is unable to detect monolayers of lead oxide so we cannot deduce its involvement in the mechanism of formation, but we may infer it.

According to Cooper, when we look at how such collectives act, we see that whether we regard statements about collectives as propositional functions or not, we cannot deduce from them statements about particular individuals.

Remark 3.2 Note that in Theorem 3.9, we cannot deduce the existence of a best proximity point unless we add another condition.

Third, we excluded records related to issues that are not addressed yet; we cannot deduce issue fix time of such records.

Then, Lemma 2.1 implies that inequality (4) holds for some α > 0. However, by using inequality (4), we cannot deduce inequality (3).

Of course, we cannot deduce any conclusion as for comparison of G and (H^{ q)}), since (1.4) is just an implication.

Hence, after obtaining Theorem 4.7, we cannot deduce Theorem 4.8 via the method of duality used by Guo et al. [2].

In this case we cannot deduce stability of the disease-free equilibrium from Theorem 4.6, since condition (1) is not satisfied.