Sentence examples for live in the domain of from inspiring English sources

Then a simple cardinality argument shows that there are 2ℵ0 real numbers which do not live in the domain of M (and so, in particular, which do not live in {m  |  M ⊨ m ∈ mˆ }).

But if X is infinite, then most of the subsets of X won't live in the domain of M (since, after all, there are 2ℵ0 subsets of X, while the domain of M is only countable).

In particular, if f and m live in the domain of M, then M ⊨ "f : ω → m is a bijection" if and only if f really is a bijection between the natural numbers and m.[22] Under its ordinary English interpretation, this formula says that the set-theoretic universe doesn't contain any bijections between the natural numbers and x.

Resnik notes that, even though M satisfies this formula, R doesn't really contain all the real numbers it only contains those real numbers which happen to live in the domain of M.[27] So, the mere fact that R is countable doesn't, in any interesting sense, generate a paradoxical situation in which the set of all real numbers is also countable.

Then we can show that there are exactly 2ℵ0 bijections f : ω → {m′ ∈ M  | M ⊨ m′ ∈ m }.[20] However, at most countably many of these bijections live in the domain of M. Hence, only countably many of them are "seen" by ∃x and ∀x under the model-theoretic interpretation of Ω x), although all 2ℵ0 of them are "seen" under the ordinary English interpretation.

In all these projects consumers were trained, assisted in ongoing curriculum review and contributed their lived experience in the domain of interest.

And you now live in the public domain in a way which others don't.

Theorists believe that the shape, or geometry, of this tiny, curled-up domain dictates the kind of universe we live in--the kind of particles that exist and the interactions between them.

Because Huck Finn lives in the public domain, outside of copyright, anyone can write another chapter in his life without penalty.

Based on an analysis of the current landscape of smart city pilot programmes, Future Internet experimentally-driven research and projects in the domain of Living Labs, common resources regarding research and innovation, can be identified that can be shared in open innovation environments.

Addresses in the dot-biz domain are expected to go live in the fall.