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

>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 ]
>
>
>
>Jack (The Wolverine) Goldberg
>Univ. of Mich
>

```

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