Re: Cantor Confusion
- From: Virgil <virgil@xxxxxxxxxxx>
- Date: Tue, 19 Dec 2006 13:39:56 -0700
In article <29569$45879e6a$82a1e228$23181@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:
Virgil wrote:
In article <1a591$458667c1$82a1e228$22650@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:
Virgil wrote:
In article <1166090594.020341.42340@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:
But for lim{x -> oo} lim{y -> oo} (2x + 3y)/(x + y) = 3
and lim{y -> oo} lim{x -> oo} (2x + 3y)/(x + y) = 2,
one cannot exchange the order of the limits without changing the value
of the result.
This is highly misleading.
What is misleading about a true and relevant statement?
Both double limits exist but they have different values.
The issue is whether such double limits are always reversible,
and the answer, as demonstrated by the example above, is "NO".
The issue is that your limits are actually an ill-posed problem.
Does HdB claim that any of the limits mentioned does not exist according
to standard delta-epsilonics?
If not then the question of equality is quite well-posed.
.
- References:
- Re: Cantor Confusion
- From: Tony Orlow
- Re: Cantor Confusion
- From: Virgil
- Re: Cantor Confusion
- From: Han de Bruijn
- Re: Cantor Confusion
- From: Virgil
- Re: Cantor Confusion
- From: Han de Bruijn
- Re: Cantor Confusion
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