Talk:Additive function

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 Field: Number theory


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.

Well, for any additive function f, we have f(1)=0. This is because 1 is coprime to 1, therefore f(1) = f(1*1) = f(1) + f(1), hence f(1) = 0. In particular for any additive f, the function g = 2^f is multiplicative ... there is no need to consider 2^(f(n)-f(1)) ... in fact I am going to change this now. —Preceding unsigned comment added by (talk) 19:12, 27 June 2009 (UTC)

Straight definition of additive[edit]

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)

logarithmic function restricted to naturals[edit]

how is it additive? or rather, how exactly do you limit the function to make it additive, if even possible?--Ghazer (talk) 23:47, 9 February 2008 (UTC)

"the function of the product is the sum of the functions", the second definition of an additive function in the article. One restricts it to the naturals not to make that property true (it is, obviously, true more generally) but because arithmetic functions are only defined on naturals. —David Eppstein (talk) 23:52, 9 February 2008 (UTC)

It seems BigOmega, Ω(54,032,858,972,279), is 4.[edit]

As of 23Apr2011, the article lists


as 3. However, my CAS lists 54,032,858,972,279 as factoring as

11^1 * 1993^2 * 1236661^1

So BigOmega(54,032,858,972,279) = 1 + 2 + 1 = 4. (talk) 04:18, 23 April 2011 (UTC) Jonathan King, Math Dept, Univ. of Florida