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Topic: analytic function problem
Replies: 76   Last Post: Oct 28, 1996 11:08 AM

 Messages: [ Previous | Next ]
 ilias kastanas 08-14-90 Posts: 443 Registered: 12/12/04
Re: analytic function problem
Posted: Oct 13, 1996 10:44 PM

In article <53rjgj\$ir8@newsbf02.news.aol.com>, Tleko <tleko@aol.com> wrote:
@In article <53oek5\$hqe@nuke.csu.net>, Ilias Kastanas wrote:
@>
@>@:>tleko wrote:
@>@:> Indeed we have z=z* .
@>@:> We write z=r.exp(i.@)
@>@:> z*=r.exp(i.(-@))
@>@:> to obtain z-z*=r.((cos@+i.sin@)-(cos(-@)+i.sin(-@-pi))) = 0 .
@
@>@:>)@@In the article <53e100\$60r@nuke.csu.net> Ilias Kastanas wrote:
@>@:>)@@Is it possible not to realize this can only hold for y=o, i.e. for
@>@:>)@@real z, and not in general?
@>@:>
@>@:> Yes it is. 2.r.i.sin@ = 2.i.y is valid for any real y
@>@:> not only for y=0.

@> No it is not. x+iy = x-iy holds for y=0, not for "any real y"...
@
@> Of course you deleted this, and you are pretending to "answer" by
@> stating that r sin@ = y. Denial goes a far way.
@
@> How about a straight answer? Are you claiming x+iy = x-iy holds
@> for all real y? YES or NO?

@ I did NOT write x+iy=x-iy you did.

You wrote z = z* and z - z* = 0 a number of times.

It so happens that z = x + iy and z* = x - iy. If this comes as a
surprise look it up: e.g. Hewitt & Stromberg, "Real and Abstract Analysis",
p. 48, or G.H. Hardy, "Pure Mathematics", p. 82.

In those same pages, by the way, you will discover that Re(z) = x
and, wonder of wonders, Im(z) = y.

Equality can be so inconvenient... You claimed z = z*, and thus
x + iy = z = z* = x - iy. Do you insist on it, yes or no?

@ I wrote in the article <531615\$emo@newsbf02.news.aol.com>:
@ z=r.exp(i.@) , z*=r.exp(i.(-@))

Say, r = sqrt(2), @ = pi/4, z = 1 + i, z* = 1 - i. What sort
of hallucination can possibly suggest that 1 + i = 1 - i ?

@ to obtain z-z*=r.((cos@+i.sin@)-(cos(-@)+i.sin(-@-pi)))=0
@
@ < where Imag(z*)=r.sin(-atan(y/x)-pi)=r.sin(atan(y/x)) >.

This is wrong, and will stay wrong no matter how many times you
repeat it, or how strenuously you ignore the errors in it, errors that a
number of people pointed out.

@ It shows that x+iy and x-iy are not analytic functions in the unit
@ disk.

This is wrong, and will stay wrong no matter how many times you
repeat it, or how strenuously you ignore the numerous proofs showing
that z is analytic and z* is not.

@ I will be glad to send you the plots and the 7th volume of 'Critical
@ Comments ..' catalogued in the Library of Congress and several
@ university libraries in the United States and abroad.

@ tleko@aol.com

Thank you, but I cannot think of a more idle exercise. Plots are
irrelevant to analyticity of z or z*, to say the least. And lengthy
volumes are unnecessary for matters short and simple. If the 7th volume
or its cohorts make nonsensical claims they are nonsense, whether cata-
logued in the Library of Congress or not. If they consist of dozens of
people telling you you are wrong and you ignoring them or thanking them
for their contribution, it is hardly news.

Ilias

Date Subject Author
9/30/96 Christopher
9/30/96 David Ullrich
9/30/96 Hunter James D. STA x4202
10/1/96 David Ullrich
9/30/96 ilias kastanas 08-14-90
9/30/96 Dik T. Winter
10/1/96 David Kastrup
10/1/96 Hunter James D. STA x4202
9/30/96 Zdislav V. Kovarik
9/30/96 Anne DeCampo
10/2/96 Christopher
10/1/96 Tleko
10/2/96 David Kastrup
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 David Ullrich
10/3/96 Tleko
10/3/96 Dik T. Winter
10/3/96 Tleko
10/3/96 Zdislav V. Kovarik
10/5/96 Tleko
10/5/96 Dik T. Winter
10/6/96 Tleko
10/6/96 David Ullrich
10/7/96 ilias kastanas 08-14-90
10/7/96 Tleko
10/7/96 Andreas Leitgeb
10/7/96 Andreas Leitgeb
10/7/96 ilias kastanas 08-14-90
10/8/96 Tleko
10/8/96 Zdislav V. Kovarik
10/8/96 ilias kastanas 08-14-90
10/9/96 David Ullrich
10/8/96 Jim Hunter
10/8/96 Tleko
10/9/96 David Kastrup
10/9/96 Ilias Kastanas
10/11/96 Tleko
10/12/96 ilias kastanas 08-14-90
10/12/96 Dik T. Winter
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/11/96 Tleko
10/12/96 Tleko
10/12/96 Sue Franklin
10/13/96 Ilias Kastanas
10/13/96 Tleko
10/13/96 Tleko
10/13/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/13/96 Tleko
10/13/96 Tleko
10/14/96 ilias kastanas 08-14-90
10/14/96 Dik T. Winter
10/15/96 Tleko
10/15/96 David Kastrup
10/15/96 Ilias Kastanas
10/16/96 Tleko
10/16/96 Dik T. Winter
10/17/96 Raymond DeCampo
10/18/96 Ariel Scolnicov
10/19/96 Tleko
10/19/96 Dik T. Winter
10/20/96 Terry Moore
10/21/96 Dik T. Winter
10/22/96 Ariel Scolnicov
10/20/96 Tleko
10/21/96 Terry Moore
10/22/96 David Kastrup
10/23/96 Tleko
10/24/96 Gunter Bengel
10/28/96 David Kastrup
10/28/96 David Ullrich