Sentence examples for a theorem on the set of from inspiring English sources

We start with some definitions and continue with presenting a theorem on the set of all fuzzy semi-numbers with equivalent source functions.

In this section, we present new fixed point theorems on the setting of complete metric spaces.

Theorem Consider the set of DNA sequences having the same number (n) of nucleotides.

We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices.

Conceptually, the system settles the problem of making Cantor's distinction between inconsistent and consistent precise and applicable (against Hilbert's early criticism); it also shows that global choice becomes a theorem on a suitable view of sets.

On the other hand, some sources prefer to use a restricted Recursion Theorem that applies only to the set of natural numbers.

On the other hand, the conditions in Theorem 2 yields Algorithm 1, which predicts the set of degree 2 vertices as well as the edges adjacent to them.

How can the very axioms which prove Cantor's theorem on the existence of uncountable sets be satisfied by a model which is itself only countable?

In general, the set of theorems will not be recursively enumerable.

As the footnote on p. 527 shows, he believed that the set of all propositions is a counterexample to Cantor's theorem.

Cantor's Theorem shows that the power set (i.e., the set of all subsets) of any given set has a larger cardinality than the given set itself.