THE ALTERNATIVE ANALYSIS: ITS BASIS, THEORY AND SOME APPLICATIONS

Author(s): Sukhotin Alexander Mikhailovich

Rubric: Information technology

Release: 2014-1 (4)

Pages: 223-228

Keywords: Euclidean Axiom 8, natural numbers set, continuum-hypothesis, an injection, a sequence of natural numbers, a countable set, exact-permutation

Annotation: Let N be the positive integers set. In this paper we prove that any mapping f: N®A, with AN, cannot be an injective one, i. е. (AN)Þ(Ø(A~N)). We use the theorem about of linear n-space basis, that is there das not exists any injective mapping of basis B_(n+1)into a basis B_n. In other words, we proved Euclidean Axiom 8: “The Whole is more than its own Part”; there are some proofs this theorem in our article.

Bibliography: Sukhotin AL.MI. THE ALTERNATIVE ANALYSIS: ITS BASIS, THEORY AND SOME APPLICATIONS // Education Resources and Technologies. – 2014. – № 1 (4). – С. 223-228. doi: