Infinite arithmetical progressions and global trees in natural numbers structure

Genady Ryabov, Vladimir Serov


The article is a continuation of the natural numbers structure research on the basis of infinitary structures composition, infinite arithmetical progressions, global d-ary trees and the set of non-negative natural N. The semi-additive canonical form of natural number with the given module d is offered, on the basis of Euclid's algorithm. The definition of the global, directed 6-ary tree (GT) as a graph of nodes marking process by the sequence of natural numbers is given. The choice of the basic modules d for GT structure other than 6 is considered. It is noted also the "galactic" character of GT. The ring progression and the quasi-progression with a variable difference d, as a result of progressions merging are entered.

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