# [Maxima] Operations on inf

Jay Belanger belanger at truman.edu
Fri Mar 9 11:25:48 CST 2007

```"Stavros Macrakis" <macrakis at alum.mit.edu> writes:
...
> Agreed that when you type in 1, you mean 1.  The problem comes when we start enabling
> simplifications like 1/inf => 0.  Then as far as Maxima is concerned, it can't tell
> the difference between the 1 you typed in and the 1 that comes from 1+1/inf.  Now I
> believe we agree that (1+1/inf)^inf must be UND, since after all (1+1/x^a)^x = inf if
> a<1, %e if a=1, and 1 if a>1, so how do we avoid the incorrect simplification (1+1/
> inf)^inf => 1?
>
> As I say, there are sophisticated ways to avoid it (keep track of infinitesimals --
> though of course that doesn't cover all cases) and there are simple ways (just
> failsafe to UND).
>
> What would you propose?

I see what you're saying now (finally, you say); I had been thinking
of the results of explicitly using limits, but what happens when you
enter (1+1/inf)^inf directly?
I don't have any good ideas; I guess I'd have 1+1/inf evaluate to 1,
have 1^inf evaluate to 1, (which would make (1+1/inf)^inf = 1, I
realize) and expect the user to understand how Maxima and limits
work.
Out of curiousity, how do other CASs handle this situation?

Jay
```