| ----------------------------------------------------------
| "Jim Kelley"
| wrote in message ...
|
| [...]
|
| "X-rays will prove to be a hoax."
|
| http://zapatopi.net/kelvin/quotes/
|
| ac6xg
| ----------------------------------------------------------

A
I hope you will excuse me the next example.

Let

f = Sin[x]

I choose:

x = 2*k*pi

and k goes to infinity one by one: 0, 1, 2, ...

Definitely then I found correctly f(oo) = 0.


Cecil chooses:

x = 2*k*pi + pi/2

and k goes to infinity one by one,
as before.

Definitely he founds correctly f(oo) = +1


Lord Kelvin chose:

x = 2*k*pi - pi/2

and k went to infinity one by one,
as above.

Definitely he founded correctly f(oo) = -1


All of us
we are correct in all steps,
but the value

f(oo)

does not exist as a single one.
In fact f(oo) takes every value between -1 and +1.

f(oo) definitely depends
on the way in which each one of us
went to infinity.

IMHO:
this is the kind of behavior of Zinp.

B
But in addition to that there is one more to say:

Zinp is a result of
the order in which we consider the limits
for the wire radius and the length to wavelength ratio.

If
a is the wire radius and
L/wl is the ratio of length to wavelength
then
I can imagine five cases:

1
First the a is going to zero,
a formula is produced for Zinp,
then the L/wl is going to infinity
and a number may or may not be the result for Zinp.

2
First the L/wl is going to infinity
a formula is produced for Zinp,
then the a is going to zero
and a number may or may not be the result for Zinp.

3
Simultaneously,
both
the L/wl is going to infinity
and
the a is going to zero,
and a number may or may not be the result for Zinp.

4
We keep a constant value for L/wl,
then a is going to zero
and a number may or may not be the result for Zinp.

5
We keep a constant value for a,
then L/wl is going to infinity
and a number may or may not be the result for Zinp.

[ On the occasion I have to confess that the movie at
[ http://antennas.ee.duth.gr/ftp/visua...s/fu010100.zip
[ 850 KB
[ belongs to the last case.

For a possible conclusion
let me mention a remarkable note from a Mathematical book:

"The biggest source of erroneous conclusions
have to do with the order we consider the limits"

(and which order we tend then to forget ... )

Sincerely,

pezSV7BAXdag