Two main concepts of infinity (Aristotle's and Cantor's) are known in the history of mathematics. The last one, prevailing at present, was formulated by founder of the set theory Cantor about a century and a half ago. Cantor used (1) the diagonal method to compare the powers of the set of infinite rows of digits 0 and 1 and natural number series; (2) the Cantor's theorem about prevalence of the power of the set of all subsets of a set A over the power of A: |P(A)|>|A|. In this work it is shown by use of specific examples that Cantor's reasons can't be considered as strict proofs. Therefore, the concept of the common potential (Aristotelian) infinity seems to be more acceptable.