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Re: Limit of Floor function

• To: mathgroup at smc.vnet.net
• Subject: [mg73852] Re: Limit of Floor function
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 2 Mar 2007 06:26:40 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <es6dgu$s4l$1@smc.vnet.net>

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
> 

Limit does not check both sides of the required value. You should 
manually check the limit on the left and on the right.

In[1]:=
Limit[Floor[x], x -> 10]

Out[1]=
10

(* Limit on the right *)

In[2]:=
Limit[Floor[x], x -> 10, Direction -> -1]

Out[2]=
10

(* Limit on the left *)

In[3]:=
Limit[Floor[x], x -> 10, Direction -> 1]

Out[3]=
9

Regards,
Jean-Marc