Sentence examples for basis of mathematics from inspiring English sources
Foundations of mathematics, the study of the logical and philosophical basis of mathematics, including whether the axioms of a given system ensure its completeness and its consistency.
Inquiries into the logical and philosophical basis of mathematics reduce to questions of whether the axioms of a given system ensure its completeness and its consistency.
Following this, the sampling frame consisted of 5019 children selected on the basis of mathematics teacher ratings or web-assessed test data at age 10: 4077 with teacher ratings, 3918 with web-test data and 2976 twins with both.
Because these principles also underly Russian recursive analysis and the constructive analysis of E. Bishop and his followers, intuitionistic logic may be considered the logical basis of constructive mathematics.
The aim of the present paper is to provide an easy access to the shuffle formula on the basis of elementary mathematics.
Philosophers and mathematicians were forced to acknowledge the lack of an epistemological and ontological basis for mathematics.
This article presents the historical background of foundational questions and 20th-century efforts to construct a new foundational basis for mathematics.
The main idea is to adopt the hypothetical component as the basis for accommodating the application of mathematics.
The developments of set theory in 1960's led to an era of independence in which many of the central questions were shown to be unresolvable on the basis of the standard system of mathematics, ZFC.
For, using this machinery, it was shown that the open questions that the early descriptive set theorists were trying to answer could not be resolved on the basis of the standard axioms of mathematics, ZFC.
He, however, rejected it on the basis of his finitist conception of mathematics; since the performance of a supertask involves the successive carrying out of an actual infinity of actions or operations, and the infinity is impossible to accomplish, in his view.
