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Options for Limit.

  • To: mathgroup at
  • Subject: [mg20832] Options for Limit.
  • From: Jack Goldberg <jackgold at>
  • Date: Wed, 17 Nov 1999 03:40:47 -0500 (EST)
  • Sender: owner-wri-mathgroup at

Hi Group,

The single option for Limit is 



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 ]


(**)	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 ]


	Limit[ f[x], x->0, Direction -> Above ]

If Mathematica adopts these suggestions, world peace will soon follow :-)

Jack (The Wolverine) Goldberg
Univ. of Mich

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