Re: -- Wrong limits do not commute

G. Rodrigues wrote:

Virgil wrote:

<snip>

In the above you are not doing iterated limits, so
I've snipped it.

Yeah, that's right, "I was not doing iterated limits"
. Sigh !^@#&%!


No you were not. You contrived an approximation scheme by introducing an arbitrary cutoff somewhere along the line. Maybe (maybe) related to, but different from, iterated limits.

<snip>

Let me ask you one thing: the non-equality of
iterated limits means
geometrically that if you have a function f(x, y)
say, then examining
the behaviour of f along two different parallel
paths (meaning, they
start and end at the same points) leads to
different results. Is your
contention that every such limiting procedure along
parallel paths
should yield the same results and only fails to do
so in cunningly
contrived cases that never appear in the practical
applications of
mathematics?

How can two different parallel paths start and end at
the same points ?


This is standard terminology in some fields of mathematics. If it bothers you, replace "parallel paths" by "two paths that start and end at the same point". Now, will you or will you not please answer the question?

Regards,
G. Rodrigues
.

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