# Likeℕ’s – a point of view on natural numbers

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2017)

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

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topEdward 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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