Likeℕ’s – a point of view on natural numbers

Edward Tutaj

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2017)

  • Volume: 16, Issue: 1, page 95-115
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Edward Tutaj. "Likeℕ’s – a point of view on natural numbers." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16.1 (2017): 95-115. <http://eudml.org/doc/288519>.

@article{EdwardTutaj2017,
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.},
author = {Edward Tutaj},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Beurling numbers; distribution of prime numbers},
language = {eng},
number = {1},
pages = {95-115},
title = {Likeℕ’s – a point of view on natural numbers},
url = {http://eudml.org/doc/288519},
volume = {16},
year = {2017},
}

TY - JOUR
AU - Edward Tutaj
TI - Likeℕ’s – a point of view on natural numbers
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2017
VL - 16
IS - 1
SP - 95
EP - 115
AB - 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.
LA - eng
KW - Beurling numbers; distribution of prime numbers
UR - http://eudml.org/doc/288519
ER -

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