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.
@article{bwmeta1.element.doi-10_1515_aupcsm-2017-0008,
author = {Edward Tutaj},
title = {Like$\mathbb{N}$'s -- a point of view on natural numbers},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {16},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2017-0008}
}
Edward Tutaj. Likeℕ’s – a point of view on natural numbers. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 16 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_aupcsm-2017-0008/