Sentence examples for mathematical statement from inspiring English sources

It was difficult to assign political meaning to a mathematical statement".

According to this principle, every mathematical statement is either true or false; no other possibility is allowed.

Under the assumptions 1 and 2, Gödel constructed a mathematical statement g that is true but not provable.

A third advantage lies in its elegance: the neoclassical theory of distributive shares lends itself to a relatively simple mathematical statement.

This journey from particular definition to abstract and universal mathematical statement has been taken as emblematic of the development of civilized life.

In particular, the consistency of mathematics, which may be taken, for instance, to be the metamathematical assertion that the mathematical statement 0 = 1 is not provable, ought to be a metatheorem that is, provable within the syntax of mathematics.

In addition, mathematics has a metalanguage; that is, names for mathematical statements and other parts of syntax, self-reference, proof and truth.

As will become clear below, it is common that nominalization strategies for mathematics change either the syntax or the semantics of mathematical statements.

The nominalistic account of mathematics that will now be discussed holds that all existential mathematical statements are false simply because there are no mathematical entities.

For example we can consider misinterpretations I of a fully interpreted sentence S. A misinterpretation of S that makes it true is known as a nonstandard or unintended model of S. The branch of mathematics called nonstandard analysis is based on nonstandard models of mathematical statements about the real or complex number systems; see Section 4 below.

Philosophical views concerning the ontology of mathematics run the gamut from platonism (mathematics is about a realm of abstract objects), to fictionalism (mathematics is a fiction whose subject matter does not exist), to formalism (mathematical statements are meaningless strings manipulated according to formal rules), with no consensus about which is correct.