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Talk:Additive function

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This is an old revision of this page, as edited by Woodstone (talk | contribs) at 21:39, 27 January 2006 (Straight definition of additive). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

There is no need to "agree that Ω(1) = 0" since that follows from the defintion: 1 has no prime factors. Also, there is no need to present two definitions for ω(n), with a verbose summation formula, since it can be expressed in a short sentence in words, just like with Ω(n). AxelBoldt

Yes as someone wish. My opinion is that well defined and written formulas tells a lot more than just words. Sometimes only formulas are left, specially in physics, as Janez Strnad once wrote. And acceptance of Ω(1) = 0 does not hurt either :) but let it stay as it is now... (I really don't mind, if you (someone) do). --XJamRastafire 23:10 Sep 19, 2002 (UTC)
We could also write to be even more clearer ... we also agree that Ω(1) = 0, since 1 has no prime factors .... Math is hard subject and never hurts one or three more words.

Straight definition of additive

The straight definition of an additive function is that it preserves the addition operation. That does not imply a numeric function and certainly not a polynomial. There is no need for a multiplication to be defined. For example the string concatenation (often denoted by "+") supports additive functions. For example UPCASE. Your definitions are unnecessarily limiting. −Woodstone 21:39, 27 January 2006 (UTC)[reply]

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