# [Maxima] limit(1/x, x, 0) => infinity

Stavros Macrakis macrakis at alum.mit.edu
Mon Dec 22 10:26:39 CST 2008

```On Mon, Dec 22, 2008 at 10:40 AM, Michael Abshoff <

>  (b) it makes me mathematically very uncomfortable that the limit of
> 1/x at 0 is infinity since the limit IMHO clearly does not exist....

a calculus student would consider the result
> incorrect IMHO.
>

Under the standard definitions, for real infinity, limit(f(x),x,a)=inf means
that for all real E there exists a real D>0 such that for all x, abs(x-a)<D
implies f(x)>E.  For complex infinity, limit(f(x),x,a)=infinity means that
for all real E there exists a real D>0 such that for all x, abs(x-a)<D
implies abs(f(x))>E.

So it is perfectly correct that limit(1/x,x,0)=infinity.

The only peculiarity of this is that Maxima works by default in the reals,
so you would not expect a complex infinity to come out of a real limit.
That is the argument for preferring UND to INFINITY.

-s
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