Sentence examples for mathematical assertion from inspiring English sources
More fundamentally, intuitionism is best seen as a theory about mathematical assertion and denial.
The book's "lucidity," he wrote — the idea that a mathematical assertion could "be proved with such certainty that any doubt appeared to be out of the question" — provoked "wonder of a totally different nature".
The statement (C) is a mathematical assertion between two abstract objects and so, in principle, the correctness maybe established mathematically.
Variables are also used to express generality, as in the mathematical assertion that for any natural number x, there is a natural number y, such that y>x and y is prime.
With Husserl, Gödel saw the problem of mathematical evidence, i.e., the question: what sort of data should count as evidence for the truth of a mathematical assertion, as fundamental.
Recently, it has been shown that within the framework of classical replicator dynamics, the MinxEnt principle is a rigorous mathematical assertion that precisely describes the replicator dynamics [ 3, 5].
It is, instead, intuitionistic logic, that is, the logic derived from the constructive interpretation of mathematical assertions.
Any topos may be conceived as possible "universe of discourse" in which mathematical assertions may be interpreted and mathematical constructions may be performed.
Mathematical assertions are rendered interpretable in a topos E by expression within E's internal language — a type-theoretic version of the usual language of set theory.
As for mathematical assertions, such as the Continuum Hypothesis in set theory, once conceptual analysis has been carried out in the right way, that is, once the basic concepts, such as that of "set," have been completely clarified, the Continuum Hypothesis should be able to be decided.
Field defends this premise by observing that "the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time" (Field 1989, p. 68) and thus are causally isolated from us even in principle.
