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Re: Limit[f[x], x->a] vs. f[a]. When are they equal?

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On 5/2/2011 6:49 AM, Andrzej Kozlowski wrote:

...
> I guess I would prefer the answer ComplexInfinity but this is not necessary since, for example, Sin[x]/x also returns Indeterminate rather than 1 at 0.

I think you mean ... at ComplexInfinity.

>   This is the kind od thing any user can decide for himself   by explicitly defining g[ComplexInfinity]=ComplexInfinity.
>
> There is absolutely nothing here that in any way disagrees with any mathematics I know of.
let r[x_]:=Sin[x]/x.

Limit[r[x],x->Infinity]  is 0
Limit[r[x],x->ComplexInfinity]    is unevaluated.

r[x] /. x-> Infinity is 0
r[x] /. x->ComplexInfinity is Indeterminate

r[Infinity] is  Interval[{0,0}]   (!!!! version 7.0, anyway)

FullSimplify[%]  leaves that unchanged, but
Interval[{0,0}]==0  is True.
Interval[{0,0}]===0 is False
Interval[0]==0  is True




Indeterminate === Indeterminate   is True

Indeterminate == Indeterminate is unevaluated.

This is kind of interesting, to have two things which are identical but 
not equal.

It is difficult to deal with something that is indeterminate, when it is 
actually represented in the computer by something determinate, namely 
the symbol Indeterminate. Having a indexed set of Indeterminates (as I 
have proposed), solves some of these problems.

It depends on what mathematics you know.

RJF

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Re: Limit[f[x], x->a] vs. f[a]. When are they equal? Richard Fateman <fateman@eecs.berkeley.edu> - 2011-05-03 09:48 +0000

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