Sentence examples for as a mathematical statement from inspiring English sources

Conversely, according to the verificationist school, a scientific statement is significant only if it is a statement of logic (such as a mathematical statement deduced from axioms) or if the statement can be verified by experience (Ayer, 1936).

The full-blooded platonist recognizes a mathematical statement S as 'objectively correct' only if S is true in all mathematical structures answering to our 'full conception' of the relevant mathematical structure.

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

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

As Hilbert had put it, was there a definite method, a mechanical process that could be applied to a mathematical statement … to determine if or not it was provable?

The truth of a mathematical statement can only be conceived via a mental construction that proves it to be true, and the communication between mathematicians only serves as a means to create the same mental process in different minds.

It is expressed in terms of probability – a mathematical statement about the probability of an occurrence (Miller, 1995).

Applied to a true mathematical statement, at least one that the platonist recognizes as true, the result will be a true statement even according to the mathematical fictionalist.

It might be possible to strengthen the results of the rule of thumb to obtain a rigorous mathematical statement.

He felt that once this was done, there would be an "effective procedure", i.e., an algorithm that would take as input any precise mathematical statement, and, after a finite number of steps, decide whether the statement was true or false.

Hence, as noted, existential mathematical statements, such as 'there are infinitely many prime numbers', are false.