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

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ilias kastanas 08-14-90

Posts: 443
Registered: 12/12/04
Re: analytic function problem
Posted: Oct 13, 1996 10:44 PM
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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
Read analytic function problem
Christopher
9/30/96
Read Re: analytic function problem
David Ullrich
9/30/96
Read Re: analytic function problem
Hunter James D. STA x4202
10/1/96
Read Re: analytic function problem
David Ullrich
9/30/96
Read Re: analytic function problem
ilias kastanas 08-14-90
9/30/96
Read Re: analytic function problem
Dik T. Winter
10/1/96
Read Re: analytic function problem
David Kastrup
10/1/96
Read Re: analytic function problem
Hunter James D. STA x4202
9/30/96
Read Re: analytic function problem
Zdislav V. Kovarik
9/30/96
Read Re: analytic function problem
Anne DeCampo
10/2/96
Read Re: analytic function problem
Christopher
10/1/96
Read Re: analytic function problem
Tleko
10/2/96
Read Re: analytic function problem
David Kastrup
10/3/96
Read Re: analytic function problem
Dik T. Winter
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
David Ullrich
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
Dik T. Winter
10/3/96
Read Re: analytic function problem
Tleko
10/3/96
Read Re: analytic function problem
Zdislav V. Kovarik
10/5/96
Read Re: analytic function problem
Tleko
10/5/96
Read Re: analytic function problem
Dik T. Winter
10/6/96
Read Re: analytic function problem
Tleko
10/6/96
Read Re: analytic function problem
David Ullrich
10/7/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/7/96
Read Re: analytic function problem
Tleko
10/7/96
Read Re: analytic function problem
Andreas Leitgeb
10/7/96
Read Re: analytic function problem
Andreas Leitgeb
10/7/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/9/96
Read Re: analytic function problem
Simon Read
10/8/96
Read Re: analytic function problem
Tleko
10/8/96
Read Re: analytic function problem
Zdislav V. Kovarik
10/8/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/9/96
Read Re: analytic function problem
David Ullrich
10/8/96
Read Re: analytic function problem
Jim Hunter
10/8/96
Read Re: analytic function problem
Tleko
10/9/96
Read Re: analytic function problem
David Kastrup
10/9/96
Read Re: analytic function problem
Ilias Kastanas
10/11/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/12/96
Read Re: analytic function problem
Dik T. Winter
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/11/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
Tleko
10/12/96
Read Re: analytic function problem
Sue Franklin
10/13/96
Read Re: analytic function problem
Ilias Kastanas
10/15/96
Read Re: analytic function problem
Simon Read
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/14/96
Read Re: analytic function problem
Dik T. Winter
10/13/96
Read Re: analytic function problem
Tleko
10/13/96
Read Re: analytic function problem
Tleko
10/14/96
Read Re: analytic function problem
ilias kastanas 08-14-90
10/14/96
Read Re: analytic function problem
Dik T. Winter
10/15/96
Read Re: analytic function problem
Tleko
10/15/96
Read Re: analytic function problem
David Kastrup
10/15/96
Read Re: analytic function problem
Ilias Kastanas
10/16/96
Read Re: analytic function problem
Tleko
10/16/96
Read Re: analytic function problem
Dik T. Winter
10/17/96
Read Re: analytic function problem
Raymond DeCampo
10/18/96
Read Re: analytic function problem
Ariel Scolnicov
10/19/96
Read Re: analytic function problem
Tleko
10/19/96
Read Re: analytic function problem
Dik T. Winter
10/20/96
Read Re: analytic function problem
Terry Moore
10/21/96
Read Re: analytic function problem
Dik T. Winter
10/22/96
Read Re: analytic function problem
Ariel Scolnicov
10/20/96
Read Re: analytic function problem
Tleko
10/21/96
Read Re: analytic function problem
Terry Moore
10/22/96
Read Re: analytic function problem
David Kastrup
10/23/96
Read Re: analytic function problem
Tleko
10/24/96
Read Re: analytic function problem
Gunter Bengel
10/28/96
Read Re: analytic function problem
David Kastrup
10/28/96
Read Re: analytic function problem
David Ullrich

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