# 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 AN, cannot be an injective one, i. е. (AN)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: