Re: ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg56918] Re: [mg56878] ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?*From*: Chris Chiasson <chris.chiasson at gmail.com>*Date*: Tue, 10 May 2005 03:42:20 -0400 (EDT)*References*: <200505090545.BAA13789@smc.vnet.net>*Reply-to*: Chris Chiasson <chris.chiasson at gmail.com>*Sender*: owner-wri-mathgroup at wolfram.com

I don't know about other version, but the following makes me worried: In[1]:= Limit[ArcTan[1/x],x->0]==Limit[ArcTan[1/x],x->0,Direction->-1] Out[1]= True In[2]:= Limit[ArcTan[1/x],x->0]==Limit[ArcTan[1/x],x->0,Direction->1] Out[2]= False In[3]:= $Version Out[3]= 5.0 for Microsoft Windows (November 18, 2003) Isn't there a requirement that the right and left limits match before a limit exists? On 5/9/05, steve <nma124 at hotmail.com> wrote: > hi; > Mathematica 5.1, on windows. > > ArcTan[1/0] gives an error but > ArcTan[Infinity] gives the correct answer. > > One way to make ArcTan[1/0] give Pi/2 is to > write it as ArcTan[0,1]. > > I do know that 1/0 is DirectedInfinity[] with > unknown direction while Infinity is > DirectedInfinity[1], and that is probably the > reason that ArcTan[1/0] gives an error > but ArcTan[Infinity] does not. > > I am asking is how to make 1/0 result in DirectedInfinity[1] > to avoid the error? is this possible? > > What function do I need to wrap 1/0 with to > cause it to become Infinity[1] instead of > Infinity[] ? or may be I need to figure how > to detect if a division results in Infinity[] > and convert that to Infinity[1]? do I need > to redfine 1/0 somehow? may be make a new > rule to say if Mathematica see 1/0 expression then > make it Infinity[1]? but may be this will screw > other things? > > Or may I should not mess with this stuff and > just change the code to ArcTan[x,y] instead of > ArcTan[y/x] and be happy? > > thanks, > Steve > > -- Chris Chiasson http://chrischiasson.com/ 1 (810) 265-3161

**References**:**ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?***From:*"steve" <nma124@hotmail.com>