Sentence examples for arithmetical proof of from inspiring English sources

The history of mathematics has shown that making a "detour" through higher mathematics can sometimes lead to a proof of an arithmetical statement that is much shorter and that provides more insight than any purely arithmetical proof of the same statement.

In 1931, Austrian mathematician Kurt Gödel's Incompleteness Theorems showed that an arithmetical proof cannot be both complete and internally consistent within itself.

In the Gödelian context of arithmetical proofs, the problem was coped with by a general method of assigning arithmetical semantics to self-referential assertions \(c : A ( c)\) stating that \(c\) is a proof of \(A ( c)\).

The modal completeness theorem by Segerberg was an important first step in Solovay's proof of arithmetical completeness of GL with respect to Peano Arithmetic.

Segerberg showed that GL is complete even with respect to the more restricted class of finite transitive irreflexive trees, a fact which later turned out to be very useful for Solovay's proof of the arithmetical completeness theorem (see Section 4).

According to him, Schröder's idea of solving a relational equation was a precursor of Skolem functions, and Schröder inspired Löwenheim's formulation and proof of the famous theorem that every "arithmetical" sentence with an infinite model has a countable model.

For statistical analysis, the arithmetical mean day-of-year of onset of each stage was calculated for each treatment.

Through this, comparability therefore transfers to the alephs, and Cantor was able to give clear and appropriate arithmetical operations of addition, multiplication and exponentiation, generalising the corresponding notions for finite collections, and the statement and proof of general laws concerning these.

The proof of everything.

This was proof of life.

Proof of U.S. residency suggested.