<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We define and study some simple structures which we call <italic>likens</italic> and which are conceptually near to <italic>both</italic> 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 <italic>space of likens</italic>. A similar idea is known for a long time as <italic>the Beurling generalized numbers</italic>. Our approach may be considered as a little more natural and more general, since it admits the <italic>finitely generated likens</italic>.</p></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 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.

Likeℕ’s – a point of view on natural numbers

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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{"article-title":"Likeℕ\u2019s \u2013 a point of view on natural numbers"}

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* =...

Likeℕ’s – a point of view on natural numbers

Published Online: Jan 27, 2018

Page range: 95 - 115

Received: Nov 05, 2017

Accepted: Nov 29, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0008

Keywords
Beurling numbers, distribution of prime numbers

© 2017 Edward Tutaj, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Likeℕ’s – a point of view on natural numbers

Published Online: Jan 27, 2018

Page range: 95 - 115

Received: Nov 05, 2017

Accepted: Nov 29, 2017

DOI: https://doi.org/10.1515/aupcsm-2017-0008

KeywordsBeurling numbers, distribution of prime numbers

© 2017 Edward Tutaj, published by De Gruyter Open

This work is licensed under a Creative Commons Attribution Share-Alike 4.0 License.

Keywords
Beurling numbers, distribution of prime numbers