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Re: Limit of Floor function

• To: mathgroup at smc.vnet.net
• Subject: [mg73886] Re: [mg73830] Limit of Floor function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 2 Mar 2007 06:45:02 -0500 (EST)
• References: <200703011121.GAA28373@smc.vnet.net>

On 1 Mar 2007, at 12:21, Eric Smith 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?
>
> Thanks,
> Eric
>


Mathematica's Limit computes directional limits only (Limit[f[x]-,x- 
 >a] is the same as Limit[f[x],x->a, Direction -> -1]). Using  
explicit values for the Direction option we get


Limit[Floor[x],x->10,Direction->-1]

10


Limit[Floor[x],x->10,Direction->1]

9

Both of these are correct answers.

Andrzej Kozlowski

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