# Talk:Divisibility

From Citizendium, the Citizens' Compendium

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 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.

- 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.

- 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)