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:"An arithmetic function is any real- or complex-valued function defined on the set N of positive integers. (In other words, an arithmetic function is just a sequence of real or complex numbers, though this point of view is not particularly useful)", see [http://www.math.illinois.edu/~ajh/ant/main1.pdf].[[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 08:15, 8 June 2017 (UTC)
:: ... I added three classical references giving this less restrictive definition, and modified the lead accordingly. [[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 15:41, 8 June 2017 (UTC)
::: I am sort of unhappy with this change. The previous version suffered from being not a precise definition but still morally accurate: the point of the name "arithmetic function" is that it expresses something about arithmetic, of interest to number theorists. The new definition does actually define something, but it is morally wrong: no one is really interested in the collection of all sequences of complex numbers, the vast majority of which have no meaning whatsoever for number theory (or for anything else). {{u|Sapphorain}}, do the sources you've added have more discussion of this definition, along the lines of the quote in your first comment, that could be used to explain that the cultural/historical background is important in the use of the name (not just a formal definition)? --[[User:Joel B. Lewis|JBL]] ([[User_talk:Joel_B._Lewis|talk]]) 20:44, 8 June 2017 (UTC)
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