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== Revert ==
I changed the article back to the previous version for the following reasons:
* It used '''N''' for the positive integers, but we generally use that symbol for the non-negative integers, see [[natural number]].
://1 '''Z'''<sup>+</sup>≡'''N'''. Non-negative are (or should be) denoted '''Z'''<sup>*</sup>. ('''Z'''<sup>*</sup>=0+'''N''')
::In Wikipedia, '''N''' stands for the non-negative integers, as [[natural number]] explains. We have to use consistent conventions, even if they are arbitrary.[[user:AxelBoldt|AxelBoldt]]
::://2 I am not quite shure if above is really so well explained in subsistent wikipedian article [[natural number]]. About '''consistent''' conventions I won't argue - according to Ribenboim (1996) this matter about what natural numbers should be is not so important and it is dependent on the usage of the definitons. Famous French "group mathematician" [[Bourbaki]] and many more used 0 as natural number like Wikipedia. Others don't. For instance [[Moebius function|Möbius function]] μ(0) is trivial and it does not show any real properties of the function itself. I am now confused even more, but I would like to use consistent stuffs in math still...
::::Yes, what counts as a "natural number", and what is denoted by '''N''', is a matter of convention. There are two competing coventions: number theorists reserve "natural number" and '''N''' for "positive integer", Bourbaki, set theorists and computer scientists reserve "natural number" and '''N''' for "non-negative integer". At one point, we in Wikipedia decided to follow the second convention. If that is not clear from [[natural number]], we have to clarify that entry. [[user:AxelBoldt|AxelBoldt]]
::::://3 Would it be OK to add somewhere in natural number a simple table like this (non-Wikipedian conventions!):
::::: ''integers'' {-∞...,-2,-1,0,1,2,...,+∞} '''Z'''
::::: ''positive integers'' {1,2,...,+∞} '''Z'''<sup>+</sup> ≡ '''N'''
::::: ''non-negative integers'' {0,1,2,...,+∞} '''Z'''<sup>*</sup> ≡ 0+'''N'''
::::: ''non-positive integers'' {-∞...,-2,-1,0} /*no designation */ ≡ '''Z'''-'''N'''
::::: ''negative integers'' {-∞...,-2,-1} '''Z'''<sup>-</sup> ≡ '''Z'''-'''Z'''<sup>*</sup>
:::::: No, that would not be ok, because then people could think that Wikipedia uses '''N''' for positive integers, which it doesn't. I will add symbols to [[number]]. [[user:AxelBoldt|AxelBoldt]]
* No need for colors in formulas.
://1 Red color was mentioned for unshure statement lately when cleared up put out.
::You used green for a function arrow.[[user:AxelBoldt|AxelBoldt]]
::://2 I saw two colors in formulas (blue and magenta) like this:
:::ln x <sup>[[e]]</sup>.
:::Why other colors are so scandalous? Where can I find that I can't use colors in math formulas? We should create something like '''/mathematics/how to write formuals, etc'''. I think I am violating nothing here...
* The definition of Ψ didn't make sense: in one equation the function Ψ took two arguments, in the other it took only one. Furthermore, this does not seem to be an accepted use of the term "arithmetic function".
://1 DNA (Do not agree) Number of arguments are obviously proper property of this function. Another definition won't hurt noone. It would make him to think a little bit.
::A function either takes two arguments or one. Your definition did not make sense, because it mixed the two. It didn't specify what the ___domain and codomain of Ψ is.[[user:AxelBoldt|AxelBoldt]]
://2 Says who? A god Math Zeus a.k.a. Axel?
::I signed my statement, so you know who said it. Why play rhethorical games like this? [[user:AxelBoldt|AxelBoldt]]
::://3 I think above is not true. In the first example function Ψ(m+n) has two parameters ''m'' and ''n'' if we watch that before adding them and it has one argument, let us say ''s''=''m''+''n''. This is OK for me. In the second term of definition I guess it was not well understood. I think (we should check this) that Ψ(''m'',''n'') should be written as Ψ(''m''|''n'') or as pascalike Ψ(''m''DIV''n''). In this way function Ψ(<font color=cyan> '''X''' </font>) has the same number of parameters, where <font color=cyan> '''X''' </font> can be whatever. About games. I didn't choose them. I advise you to check your own corrections of articles of the other authors. See bellow for the same matter on mathematical insignificance.
* "Arithmetical function" was not explained.
://1 See article.
::://2 I tried to explain that but obviously that was not explanation. Don't know what to do futher on. I saw in many ways that someone uses two different terms arithmetic(al) functions but I do not want to impose my opinions to anyone. And I have rights on my own opinions, do I?
[[user:AxelBoldt|AxelBoldt]], Thursday, April 18, 2002
://1 How to move from the NPOV in this way?
://2 It is very easy to find 1001 reasons to revert one extended (not necessarily correct) article to previous state. --[[user:XJamRastafire|XiJam]] [2002.04.18] 4 Thursday (0). <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:XJaM|XJaM]] ([[User talk:XJaM#top|talk]] • [[Special:Contributions/XJaM|contribs]]) 08:57, 18 April 2002 (UTC)</small>
I removed this again:
''Another definition of arithmetic function is a function with exactly two [[composition|compositional properties]]:''
:Ψ(''m''+''n'') = Ψ[Ψ(''m'')+Ψ(''n'')] <tt> /composition with addition/ </tt>
:Ψ(''m'',''n'') = Ψ[Ψ(''m'')Ψ(''n'')] <tt> /composition with parameter/ </tt>
In the first equation, Ψ is used as a function of a single argument, in the second equation it is used as a function of two arguments. This definition is mathematically meaningless. [[user:AxelBoldt|AxelBoldt]]
XJam, where did you find these two lines involving Ψ? Maybe I can clarify it from the source. [[user:AxelBoldt|AxelBoldt]]
::::://1 At Eric's "cooking's place" http://mathworld.wolfram.com/ArithmeticFunction.html. We better go and kick his ass a little bit, ha, ha. That definition is really quite tedious, so I don't believe it would help you very much. I'll go check somewhere else.
I removed this:
:'''Note:''' Arithmetic function should not be confused with a function sometimes called ''arithmetical function'' which is in fact [[integer function]] (''f'' : '''N''' <font size=+1 color=darkgreen> → </font> '''N''').
There is no such distinction between "arithmetical" and "arithmetic" functions in the literature. Furthermore, the above arithmetical functions also qualify as arithmetic functions of course. [[user:AxelBoldt|AxelBoldt]]
::://1 No comment. --[[user:XJamRastafire|XJamΨ]] [2001.04.19] 5 Friday (0). <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:XJaM|XJaM]] ([[User talk:XJaM#top|talk]] • [[Special:Contributions/XJaM|contribs]]) 07:10, 19 April 2002 (UTC)</small>
:::::AO --[[user:XJamRastafire|XJamτ]] [2001.04.19] 5 Friday (1st ed). <!-- Template:Unsigned --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:XJaM|XJaM]] ([[User talk:XJaM#top|talk]] • [[Special:Contributions/XJaM|contribs]]) 08:24, 19 April 2002 (UTC)</small>
== Arithmetic vs arithmetical ==
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