In this work I make the analysis of the possibility of the existence of the number system with non-natural base & its investigation. The question examined in my work is totally opened:\r
‧ making the list of new characteristics, rules of the translation of the numbers, and also rules of the simple calculating operations, checked the operations of subtraction & division;\r
‧ checked the Euclidean algorithm, its characteristics by means of estimating the coefficients;\r
‧ found the practical appliance of new method in compiling & solving of the tasks.\r
Investigation I’ve suggested stipulates for independence of new system & its appliance in type of tasks, that is beyond the course of school program & also beyond the whole system of school education.
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