Davydov, N. A. Two equivalent definitions of a sequence of complex numbers. (English. Russian original) Zbl 0656.40005 Sov. Math. 30, 25-27 (1986); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 12(295), 19-21 (1986). On p. 164 of the Russian translation of J. R. Cook’s book [Infinite matrices and spaces of sequences (1960; Zbl 0091.110)], the translator - I. I. Volkov - correctly pointed out the defect in the second definition of the kernel of the sequence of complex numbers, which - according to the author’s statement - would bee equivalent to the first definition, formulated on p. 161. The defect in the second definition, as Volkov correctly notes, is covered by the fact that a definition of the barrier line for the set of partial limits of the sequence is given in it in explicit form. However, Volkov does not show how to correct this second definition, such that the two different definitions of the kernel are equivalent. In this paper we do so. MSC: 40A99 Convergence and divergence of infinite limiting processes Keywords:sequence of complex numbers; kernel Citations:Zbl 0091.110 PDFBibTeX XMLCite \textit{N. A. Davydov}, Sov. Math. 30, 25--27 (1986; Zbl 0656.40005); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1986, No. 12(295), 19--21 (1986)