The open sets of " A " ? are precisely the sets expressible as unions of these basic open sets.
32.
Such lists sometimes need customized naming, if they are not naturally expressible as alphabetic or numeric ranges, e . g.
33.
In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems.
34.
In explicit form they are expressible in terms of Jacobian elliptic functions which are periodic functions ( effectively generalisations of trigonometrical functions ).
35.
Since an infinite descent is impossible, we conclude that x must be expressible as a sum of two squares, as claimed.
36.
By the Mostert Shields theorem, every continuous t-norm is expressible as the ordinal sum of Archimedean continuous t-norms.
37.
But this meta-principle speaks about any property, that " is expressible " in at least one conceivable language.
38.
I . e ., the pole order is expressible by the rank of the groups of invertible regular functions and the Picard group.
39.
The general adoption of class variables of quantification ushers in a theory whose laws were not in general expressible in the antecedent levels of logic.
40.
In this case, each element of S is expressible uniquely as an algebraic combination of an element of V and an element of W.
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