Talk:Arithmetic function: Difference between revisions

Revision as of 00:52, 6 January 2021

Revision as of 00:54, 6 January 2021

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:::: Yes, they are not arithmetical functions because they are defined on real positive numbers. I just don't understand these two last objections. If most classical introductory courses define an arithmetical function as any function whose ___domain are the positive integers (I cited 3 books, as well as a UIUC course in the talk page), I don't very well see how this could not be mentioned at all in the lead. Not mentioning it is equivalent to giving a wrong information. [[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 19:06, 11 June 2017 (UTC)

::::: Sorry, you are completely right, I was very confused. --[[User:Joel B. Lewis|JBL]] ([[User_talk:Joel_B._Lewis|talk]]) 23:17, 19 June 2017 (UTC)

:::::: However, I am still confused, as natural numbers (the set N of positive integers) is a subset of real positive numbers. On the other hand the precise textbook definition mentioned above, ''the set of arithmetical function with the operations of addition and Dirichlet convolution is a unitary ring'' suggests that maybe it should actually be read "inside-out" as: ''arithmetic functions are precisely that subset of functions in the set of N -> C functions (sequences) whose pointwise addition and Dirichlet convolution form a unitary ring''. See also [[Dirichlet_convolution#Properties]]. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.203.239.75|82.203.239.75]] ([[User talk:82.203.239.75#top|talk]]) 00:52, 6 January 2021 (UTC)</small> <!--Autosigned by SineBot-->

== Arithmetic function ==