Sentence examples for arithmetic and its from inspiring English sources

However, the applicability of the incompleteness theorems can be dramatically extended outside the language of first-order arithmetic and its extensions, when it is noted that all that is needed is that weak theories such as Q, or PRA, can be interpreted in the system in question.

The complex nature of arithmetic and its foundational value for mathematics are well known by mathematicians and mathematics educators.

● How does your curriculum develop understanding of the structural features of whole number arithmetic and its extensions?

For example, the Axiom of Choice allows the taking of maximal ideals in rings and other structures; it entails the kinds of maximality principles that even the analysts were already using; it simplifies transfinite arithmetic; and despite its suspicious abstractness it turns out to be equivalent to 'concrete' and 'mathematical' statements such as the claim that every vector space has a basis.

The most important feature of this new method is the simplicity of arithmetic operations, and its robustness for cases where there is limited information to provide a good assessment.

On Conjectures moves directly into arithmetic and geometry with its conjectural reflections on the decade's embracing all number and with its ordering of reality's oneness and otherness using the spatial diagrams P and U that employ cones and spheres.

A Cablevision spokesman declined to grade YES's arithmetic and stood by its numbers.

In the Treatise, Hume says that geometry is not quite as certain as arithmetic and algebra, because its original principles derive from sensation, and about sensation there can never be absolute certainty.

Abstract: We will discuss the conjecture of Birch and Swinnerton-Dyer, which predicts deep connections between the L-function of an elliptic curve and its arithmetic, and the vast conjectural generalizations for motives due to Beilinson, Bloch and Kato.

I am interested in Chow groups of algebraic varieties and the relationship between a variety's Chow groups and its arithmetic and geometric properties.

Mathematical calculi do not require extra-mathematical applications, Wittgenstein argues, since we "can develop arithmetic completely autonomously and its application takes care of itself since wherever it's applicable we may also apply it" (PR §109; cf. PG 308, WVC 104).