# [Maxima] ind and und

Stavros Macrakis macrakis at alum.mit.edu
Fri Sep 25 14:22:26 CDT 2009

```The ind and und documentation is a bit terse, so here is a longer
explanation.

limit(...) -> ind means that the limit is not defined or that limit cannot
determine it, but that limit can guarantee that the limit set is bounded.
limit(...) -> und means that the limit is not defined or that limit cannot
determine it, and that limit cannot prove that the limit set is bounded.

In both cases, Maxima gives a "best effort" result.  For example,
limit(sin(x)-sin(x+1/x),x,inf) gives ind, when the correct solution is 0:
limit can determine that the limit set is bounded, but was unable to
determine that it was actually the single number 0 (though a simple

I don't think there is a clear specification of when limit returns ind/und
and when it returns a noun form.  For example:

limit(sin(x)-sin(x+1/x),x,inf) => ind
limit(sin(x)-sin(x+f(x)),x,inf) => noun form (even though the result
must be bounded by [-2,2])
limit(sin(x)-sin(x+1/sin(x)),x,inf) => und (oops)

But this is a general problem with the "best effort" philosophy: und is
always, in some sense, a correct answer. It would be better if und were
reserved for "limit can prove that the limit set is not bounded".

-s
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