Natural numbers: Difference between revisions
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Relatedly, the set of integers \(\mathbb{Z}\) contains a subset \(\mathbb{Z}^+\). Sometimes this is used to mean strictly positive integers and so doesn't contain 0 and sometimes it is used to mean non-negative integers and does contain 0. | Relatedly, the set of integers \(\mathbb{Z}\) contains a subset \(\mathbb{Z}^+\). Sometimes this is used to mean strictly positive integers and so doesn't contain 0 and sometimes it is used to mean non-negative integers and does contain 0. | ||
Sometimes authors define \(\mathbb{N}\) and \(\mathbb{Z}^+\) as the same thing, either with or without zero. Sometimes authors define them differently such that \(\mathbb{N}\) contains zero and \(\mathbb{Z}^+\) does not, and sometimes authors define them differently such that \(\mathbb{N}\) does not contain zero and \(\mathbb{Z}^+\) does. | Sometimes authors define \(\mathbb{N}\) and \(\mathbb{Z}^+\) as the same thing, either with or without zero<ref>[https://twitter.com/Joel_Feinstein/status/1430881362727288834 Tweet by Joel Feinstein]</ref>. Sometimes authors define them differently such that \(\mathbb{N}\) contains zero and \(\mathbb{Z}^+\) does not, and sometimes authors define them differently such that \(\mathbb{N}\) does not contain zero and \(\mathbb{Z}^+\) does. | ||
[[Category:Conflicting definitions]] | [[Category:Conflicting definitions]] | ||
Latest revision as of 13:57, 26 August 2021
The set of natural numbers, usually written \(\mathbb{N}\), sometimes includes 0 and sometimes doesn't include 0.
Relatedly, the set of integers \(\mathbb{Z}\) contains a subset \(\mathbb{Z}^+\). Sometimes this is used to mean strictly positive integers and so doesn't contain 0 and sometimes it is used to mean non-negative integers and does contain 0.
Sometimes authors define \(\mathbb{N}\) and \(\mathbb{Z}^+\) as the same thing, either with or without zero[1]. Sometimes authors define them differently such that \(\mathbb{N}\) contains zero and \(\mathbb{Z}^+\) does not, and sometimes authors define them differently such that \(\mathbb{N}\) does not contain zero and \(\mathbb{Z}^+\) does.
