Talk:Divisibility

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 Definition A concept in elementary arithmetic dealing with integers as products of integers [d] [e]

Property 4 is currently: "if a divides b and c then it also divides a+b." Shouldn't the last sum be b+c? If not, then we do not need c, just: if a divides b, then it also divides a+b and a-b and ... Sandy Harris 10:58, 27 June 2009 (UTC)

A typo, thanks. (Is it against CZ politeness to simply correct this?) Peter Schmitt 11:38, 27 June 2009 (UTC)

Topic Already Exists

Is there some reason that this topic needed to be created even though the divisor page already exists? I like nouns referring to objects better than ones referring to relationships, so my preference is that the main page be called divisor. However the cards fall, I think one of the pages must disappear.Barry R. Smith 19:09, 22 July 2009 (UTC)

I know about the "divisor" page, but "divisibility" is a more general notion which can serve as a "parent topic". "Divisor" is not suitable for this. I agree that, in general, objects are better suited for titles (like countable set, not "countability"), but this is different, I think. "Divisibility" or "divisibility theory" are quite usual as titles for chapters in number theory books.
Moreover, I think that divisor may still serve a purpose for the elementary arithmetic meaning of "divior" in a division and in a fraction (and to "disambiguate" more advanced uses), topics that do not fit on the divisibility page. Peter Schmitt 17:31, 23 July 2009 (UTC)
I'm don't see the greater generality, when divisor is taken in the sense of a factor of an integer. If the relationship of divisibility exists, then one number is a divisor and the other is a multiple. Conversely, if one number is a divisor of another, then the relationship of divisibility exists. "Divisors" could serve equally as a title in a number theory chapter. On the other hand, multiple is a page. What would be the symmetric notion for "divisibility"? I'm interested to know what facets divisibility has that makes it more general, and deserving of its own page.
Divisor as the second number in a division appears on the division page (although it needs to be in bold). Certainly, because of these two uses and the algebraic geometry one, the divisor page should include a disambiguation.
In my mind,the situation is reversed, and divisibility could occur as a subtopic on the "divisor" page, being defined, and specifying that it induces a partial order. Either way, I still feel that one of divisibility and divisor should be the main topic, and the other should appear as a definition within that page.Barry R. Smith 19:16, 23 July 2009 (UTC)