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Re: Re: Limit of Floor function

• To: mathgroup at smc.vnet.net
• Subject: [mg73936] Re: [mg73877] Re: Limit of Floor function
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 3 Mar 2007 01:10:50 -0500 (EST)
• References: <es6dgu$s4l$1@smc.vnet.net> <200703021140.GAA03951@smc.vnet.net>

Eric Smith wrote:
 > 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.

-1, actually. As in, approach from the right.


 > I think the documentation on the Limit function should be made more
 > clear about this,

I'm pretty sure it will be in next version.


 > since it differs from the conventional mathematical
 > definition of a limit.
 >
 > Eric

Questionable. Limits are (essentially) always first seen in calc 1 and 
it is true that those are typically defined on the real line as 
two-sided entities. This is the most commonly understood convention for 
the simple reason that most people who learn it do not go on to, say, 
functions of one (or several) complex variables. I'm not convinced this 
makes it the "conventional mathematical definition".

In a private reply to another post on this topic today I put it a bit 
differently: Limits are directional by nature. Best to get used to that, 
and earlier rather than later.

To that I will add the following. If you really want a limit when faced 
with a removable singularity, use Series. (Shoot, that could almost be a 
line for a TV series.)


Daniel Lichtblau
Wolfram Research

• References:
  • Re: Limit of Floor function
    • From: Eric Smith <eric@brouhaha.com>