Geodesic
Likeℕ’s – a point of view on natural numbers
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 16 (2017).

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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 a more 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 be considered as a little more natural and more general, since it admits the finitely generated likens.
Keywords: Beurling numbers, distribution of prime numbers 
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     title = {Like\ensuremath{\mathbb{N}}{\textquoteright}s {\textendash} a point of view on natural numbers},
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Tutaj, Edward. Likeℕ’s – a point of view on natural numbers. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 16 (2017). http://geodesic.mathdoc.fr/item/AUPCM_2017_16_a3/