Sentence examples for in weak set from inspiring English sources

But in weak set theories lacking the axiom of extensionality the derivation of Excluded Middle from AC does not go through: some form of extensionality, or the existence of quotient sets for equivalence relations, needs to be assumed.

For example, it is frequently said that the universal set (an extension which is actually trivially easy to obtain in a weak set theory) is an inconsistent totality; the actual situation is merely that one cannot have a universal set while assuming Zermelo's axiom of separation.

Motorola launched a strategic review in January, following a weak set of fourth-quarter earnings that were weighed down by troubles in its handset business.

For example, the transient formed from pHP DEP (lifetime, τ = 63 ps; in water) appears as a weak set of absorptions on the tail of the pHP triplet.

But relaxing Gilbert's conditions would naturally result in another perhaps weaker set of dynamic constraints, and not in their complete absence.

It will therefore stay within Defra – the weakest department in Whitehall, with the weakest set of ministers anyone can remember.

Secondly, since the universal attractor is just the ω-limit set of an absorbing set in weak topology, the requirement of completeness of the spaces is needed.

That Apple and Google are doing what they're doing in a weak economic setting is what grabs me.

Particularly in the weak institutional set-up of the voluntary market and the very dynamic nature of the forest carbon sector, the pursuit for legitimacy is a remarkable component of standards' activities.

As was the case for region B, Bayesian support values are high (PP > 0.95) for a handful of nodes in region C that were not present or very weak in the set of ML bootstrap trees.

As shown in Figure S6(b), the largest power loss for an alternative hypothesis in the weak-clue set is only 0.4%, which corresponds to the power gain 17% in the strong-clue set.