Sentence examples for assert the existence of from inspiring English sources
If the Axiom of Infinity is reformulated to assert the existence of Vω , then the ranks proved to exist as sets by Zermelo set theory are exactly those which appear in the natural model Vω+ω of this theory.
This shows that for a solid sphere there exists (in the sense that the axioms assert the existence of sets) a decomposition into a finite number of pieces that can be reassembled to produce a sphere with twice the radius of the original sphere.
To overcome this difficulty, implicit function theorem is firstly exploited to assert the existence of the continuous desired virtual controls.
We have also demonstrated that our semantic domain is a c.p.o., with all our constructors shown to be monotonic, allowing us to assert the existence of fixpoints.
This entails that no such claim can assert the existence of, or otherwise make reference to, anything that is beyond the realm of possible perceptual experience.
In application to matters of ontology, realism is standardly applied to doctrines which assert the existence of entities of some problematic or controversial kind.
The other was the 'inflationary' approach, which posited entities corresponding to all statements, thus 'creating' or asserting the existence of things that (Berlin believed) didn't exist at all.
(A numerical sentence is a first-order sentence asserting the existence of some objects. For example, the numerical sentence that there exist at least two objects is: ∃x∃y(x ≠ y).) If van Inwagen is correct, it is indeterminate whether or not the relevant numerical sentence is true, in which case one of the constituent expressions—'∃', 'x', 'y', '~', '=' must be vague.
