LikeN's - a point of view on natural numbers

Abstract

We define and study some simple structures which we call likens and which are conceptually near to both sets of natural numbers, i.e. N with addition and N*=N\{0} with multiplication. It appears, that there are many different likens, which makes it possible to look on usual natural numbers from amore general point of view. In particular, we show that N and N* are related to some functionals on the space of likens. A similar idea is known for a long time as the Beurling generalized numbers. Our approach may beconsidered as a little more natural and more general, since it admits the finitely generated likens.

Keywords

• Beurling numbers
• distribution of prime numbers