Re: Options for Limit.
- To: mathgroup at smc.vnet.net
- Subject: [mg20871] Re: [mg20832] Options for Limit.
- From: "David Park" <djmp at earthlink.net>
- Date: Thu, 18 Nov 1999 01:09:47 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Jack, It is often not that difficult to implement more convenient notation. For example: fromBelow = 1; fromAbove = -1; f[x_] := (1 + x)(1 - UnitStep[x]) + x UnitStep[x] Limit[f[x], x -> 0, Direction -> fromBelow] 1 Limit[f[x], x -> 0, Direction -> fromAbove] 0 David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ >Hi Group, > >The single option for Limit is > > Direction->1 >or > > Direction->-1 > >I would suggest that these choices are counterintuitive >and I offer an improvement. Here is why they are "less" >than obviou. What is one's guess at the meaning of > >(*) Limit[ f[x], x->2, Direction -> 1 ] > >or, > >(**) Limit[ f[x], x->0, Direction -> -1 ] > >Are you sure? The book says that the limit in (*) is taken >from smaller values (than 2, presumably), that is, "from below". >Similarly, (**) is to be interpreted as the limit from above. >These notations are not suggestive of the meanings and this >is not good. Moreover it violates one of the professed goals >in Mathematica - clarity of notation. (Give or take some of the >cartoon notations representing infix functions, say @@@.) > >Here is an improvement(?) > > Limit[ f[x], x->2, Direction -> Below ] > >and > > > Limit[ f[x], x->0, Direction -> Above ] > >If Mathematica adopts these suggestions, world peace will soon follow :-) > > >Jack (The Wolverine) Goldberg >Univ. of Mich >