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MathGroup Archive 2007

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Re: Limit of Floor function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73877] Re: Limit of Floor function
  • From: Eric Smith <eric at brouhaha.com>
  • Date: Fri, 2 Mar 2007 06:40:09 -0500 (EST)
  • Organization: Eric Conspiracy Secret Labs
  • References: <es6dgu$s4l$1@smc.vnet.net>

I wrote:
> Mathematica 5.2 evaluates one-sided limits of the Floor function
> correctly.  But if I just ask:
>    Limit[Floor[x],x->10]
> It replies "10".  Shouldn't it tell me the limit is undefined,
> since the Floor function has a step discontinuity at every integer
> value?

Several people have explained to me in email that Mathematica doesn't
evaluate two-sided limits, and that you have to do it yourself.
Apparently if you don't specify a direction, it assumes Direction->1.

I think the documentation on the Limit function should be made more
clear about this, since it differs from the conventional mathematical
definition of a limit.

Eric


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