Most Pathological Object in Complex Analysis
Clash Royale CLAN TAG#URR8PPP
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Complex analysis is the good twin and real analysis the evil one:
beautiful formulas and elegant theorems seem to blossom spontaneously
in the complex domain, while toil and pathology rule the reals. ~ Charles Pugh
I was just wondering: What is the most pathological object/property you can think of in Complex Analysis?
EDIT: Also posted on MathOverflow as https://mathoverflow.net/questions/310418/pathology-in-complex-analysis
complex-analysis soft-question
edited Sep 13 at 9:09
YukiJ
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
 |Â
show 1 more comment
up vote
3
down vote
favorite
1
Complex analysis is the good twin and real analysis the evil one:
beautiful formulas and elegant theorems seem to blossom spontaneously
in the complex domain, while toil and pathology rule the reals. ~ Charles Pugh
I was just wondering: What is the most pathological object/property you can think of in Complex Analysis?
EDIT: Also posted on MathOverflow as https://mathoverflow.net/questions/310418/pathology-in-complex-analysis
complex-analysis soft-question
edited Sep 13 at 9:09
YukiJ
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
2
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
1
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32
 |Â
show 1 more comment
up vote
3
down vote
favorite
1
up vote
3
down vote
favorite
1
1
Complex analysis is the good twin and real analysis the evil one:
beautiful formulas and elegant theorems seem to blossom spontaneously
in the complex domain, while toil and pathology rule the reals. ~ Charles Pugh
I was just wondering: What is the most pathological object/property you can think of in Complex Analysis?
EDIT: Also posted on MathOverflow as https://mathoverflow.net/questions/310418/pathology-in-complex-analysis
complex-analysis soft-question
edited Sep 13 at 9:09
YukiJ
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
Complex analysis is the good twin and real analysis the evil one:
beautiful formulas and elegant theorems seem to blossom spontaneously
in the complex domain, while toil and pathology rule the reals. ~ Charles Pugh
I was just wondering: What is the most pathological object/property you can think of in Complex Analysis?
EDIT: Also posted on MathOverflow as https://mathoverflow.net/questions/310418/pathology-in-complex-analysis
complex-analysis soft-question
complex-analysis soft-question
edited Sep 13 at 9:09
YukiJ
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
edited Sep 13 at 9:09
YukiJ
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
edited Sep 13 at 9:09
YukiJ
1,7572624
edited Sep 13 at 9:09
YukiJ
1,7572624
edited Sep 13 at 9:09
YukiJ
1,7572624
1,7572624
asked Sep 10 at 20:30
Kezer
1,316317
asked Sep 10 at 20:30
Kezer
1,316317
asked Sep 10 at 20:30
Kezer
1,316317
1,316317
2
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
1
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32
 |Â
show 1 more comment
2
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
1
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32
2
2
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
1
1
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32
 |Â
show 1 more comment
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2
The behaviour of a complex analytic function in a neighbourhood of an essential singularity is insane. (I would also replace "good" by "easy and artificial" and "evil" by "interesting and important" in your value judgment about the twins. $ddotsmile$.)
– Rob Arthan
Sep 10 at 20:47
1
After a bit of rewording and context, this would be a decent fit for Math Overflow.
– Rushabh Mehta
Sep 10 at 20:47
@Rob Arthan, yes indeed, that's true! About your replacements, yeah I suppose you could think about that but well I just quoted what Charles Pugh said ;p
– Kezer
Sep 11 at 12:26
@RushabhMehta Hmm, then I'll consider posting it for MathOverflow! Thanks!
– Kezer
Sep 11 at 12:27
@Kezer: apologies! I didn't notice that the statement was a quotation. I stand by what I said about the value judgment, while appreciating now that it is Pugh's value judgment and not yours. I look forward to seeing the responses you get on MO.
– Rob Arthan
Sep 11 at 21:32