On 3/7/07, Daniel Lakeland <dlakelan at street-artists.org> wrote:
>
> On Wed, Mar 07, 2007 at 03:54:24PM -0500, Stavros Macrakis wrote:
>
> > Why? Both inf*inf and inf^2 go to inf regardless of how you approach
> it.
>
> if the inf^2 is going to be used in a further computation they may not
> be equivalent... such as limit(limit(x^2/(1+y^3),y,inf),x,inf) or
> something like that...
>
Please explain your example in more detail; I don't see your point.
Remember, once it's been reduced to "inf" (as opposed to the expression it
came from), it just means *any* function that goes to infinity, which could
just as well be the sqrt of some other function. That is, it is not true
that inf*inf - inf > 0. Consider for example limit( log(x)*log(x) - x , x ,
inf).
If you're trying to keep track of the "order" of infinity... well, that's
another matter. But Maxima doesn't do that. limit(log(x),x,inf) and
limit(exp(x),x,inf) both give simply inf, with no indication that one is
asymptotically larger than the other.
-s