INF, MIND, IND, and UND cannot possibly be combined in general to give exact
limit results.
IND-IND = IND not because in all cases limitset(x)=IND & limitset(y)=IND =>
limitset(x+y) is not a single number, but because for all x and y,
limitset(x+y) is *some bounded set of reals*, that is, IND. That bounded
set may have a single element, but we can't tell that just by calculations
with INDs and UNDs.
-s
On Sat, Sep 11, 2010 at 01:36, Andreas Eder <andreas_eder at gmx.net> wrote:
>
> Richard Hennessy wrote:
>
> "Clearly limit(sin(x),x,inf)=>IND and IND-IND must be IND"
>
> The first statement is clear, the second is not. Can you prove
> it?
>
> Well, that statement is clearly wrong, because for any expr with
> limit(expr(x),x,a) => IND we obviously have limit(expr(x),x,a) -
> limit(expr(x),x,a) = limit(expr(x)-expr(x),x,a) = limit(0,x,a) =
> 0.
>
> Andreas
> --
> ceterum censeo redmondinem esse delendam.
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