What is the concept of pathological function? [closed]
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mixed derivative theorem:
Mixed partial derivatives Fxy and Fyx are always equal except for pathological functions.
for using mixed derivative theorem function must be non-pathological,so i want a way to find out a function is pathological or not?
functions derivatives differential
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
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closed as unclear what you're asking by Martin R, Brahadeesh, Shailesh, user10354138, amWhy Dec 7 '18 at 10:37
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
mixed derivative theorem:
Mixed partial derivatives Fxy and Fyx are always equal except for pathological functions.
for using mixed derivative theorem function must be non-pathological,so i want a way to find out a function is pathological or not?
functions derivatives differential
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
$endgroup$
closed as unclear what you're asking by Martin R, Brahadeesh, Shailesh, user10354138, amWhy Dec 7 '18 at 10:37
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
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"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
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– Peter
Dec 7 '18 at 8:53
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What do you mean by a pathological function?
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– Falrach
Dec 7 '18 at 9:08
1
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Some context would be helpful, but its probably what peter wrote
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– klirk
Dec 7 '18 at 9:35
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If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29
add a comment |
$begingroup$
mixed derivative theorem:
Mixed partial derivatives Fxy and Fyx are always equal except for pathological functions.
for using mixed derivative theorem function must be non-pathological,so i want a way to find out a function is pathological or not?
functions derivatives differential
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
$endgroup$
mixed derivative theorem:
Mixed partial derivatives Fxy and Fyx are always equal except for pathological functions.
for using mixed derivative theorem function must be non-pathological,so i want a way to find out a function is pathological or not?
functions derivatives differential
functions derivatives differential
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
edited Dec 7 '18 at 12:09
alireza khorshidi
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
asked Dec 7 '18 at 8:51
alireza khorshidialireza khorshidi
13
13
closed as unclear what you're asking by Martin R, Brahadeesh, Shailesh, user10354138, amWhy Dec 7 '18 at 10:37
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Martin R, Brahadeesh, Shailesh, user10354138, amWhy Dec 7 '18 at 10:37
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
1
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"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
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– Peter
Dec 7 '18 at 8:53
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What do you mean by a pathological function?
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– Falrach
Dec 7 '18 at 9:08
1
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Some context would be helpful, but its probably what peter wrote
$endgroup$
– klirk
Dec 7 '18 at 9:35
$begingroup$
If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29
add a comment |
1
$begingroup$
"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
$endgroup$
– Peter
Dec 7 '18 at 8:53
$begingroup$
What do you mean by a pathological function?
$endgroup$
– Falrach
Dec 7 '18 at 9:08
1
$begingroup$
Some context would be helpful, but its probably what peter wrote
$endgroup$
– klirk
Dec 7 '18 at 9:35
$begingroup$
If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29
1
1
$begingroup$
"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
$endgroup$
– Peter
Dec 7 '18 at 8:53
$begingroup$
"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
$endgroup$
– Peter
Dec 7 '18 at 8:53
$begingroup$
What do you mean by a pathological function?
$endgroup$
– Falrach
Dec 7 '18 at 9:08
$begingroup$
What do you mean by a pathological function?
$endgroup$
– Falrach
Dec 7 '18 at 9:08
1
1
$begingroup$
Some context would be helpful, but its probably what peter wrote
$endgroup$
– klirk
Dec 7 '18 at 9:35
$begingroup$
Some context would be helpful, but its probably what peter wrote
$endgroup$
– klirk
Dec 7 '18 at 9:35
$begingroup$
If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29
$begingroup$
If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29
add a comment |
2 Answers
2
active
oldest
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I don't think there is any definition of pathological relating to functions (or any other mathematical concept). It's simply a word used informally to describe a function that behaves in a way you might not expect and thereby serves as a counterexample to some claim you might think was true. But a function one person finds pathological because it's "weird" (that's not defined either) in relation to his studies/interests might be uninteresting to another person, because it doesn't offer anything in relation to his studies/interests.
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
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add a comment |
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You can think pathological as counterintuitive. Like everywhere continuous but nowhere differentiable function, uncountalbe null set, banach-tarski paradox. And it's not the rigorous concept, so it's weird to say finding out some function is pathological or not.
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
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add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I don't think there is any definition of pathological relating to functions (or any other mathematical concept). It's simply a word used informally to describe a function that behaves in a way you might not expect and thereby serves as a counterexample to some claim you might think was true. But a function one person finds pathological because it's "weird" (that's not defined either) in relation to his studies/interests might be uninteresting to another person, because it doesn't offer anything in relation to his studies/interests.
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
$endgroup$
add a comment |
$begingroup$
I don't think there is any definition of pathological relating to functions (or any other mathematical concept). It's simply a word used informally to describe a function that behaves in a way you might not expect and thereby serves as a counterexample to some claim you might think was true. But a function one person finds pathological because it's "weird" (that's not defined either) in relation to his studies/interests might be uninteresting to another person, because it doesn't offer anything in relation to his studies/interests.
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
$endgroup$
add a comment |
$begingroup$
I don't think there is any definition of pathological relating to functions (or any other mathematical concept). It's simply a word used informally to describe a function that behaves in a way you might not expect and thereby serves as a counterexample to some claim you might think was true. But a function one person finds pathological because it's "weird" (that's not defined either) in relation to his studies/interests might be uninteresting to another person, because it doesn't offer anything in relation to his studies/interests.
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
$endgroup$
I don't think there is any definition of pathological relating to functions (or any other mathematical concept). It's simply a word used informally to describe a function that behaves in a way you might not expect and thereby serves as a counterexample to some claim you might think was true. But a function one person finds pathological because it's "weird" (that's not defined either) in relation to his studies/interests might be uninteresting to another person, because it doesn't offer anything in relation to his studies/interests.
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
answered Dec 7 '18 at 9:03
HenrikHenrik
6,03792030
6,03792030
add a comment |
add a comment |
$begingroup$
You can think pathological as counterintuitive. Like everywhere continuous but nowhere differentiable function, uncountalbe null set, banach-tarski paradox. And it's not the rigorous concept, so it's weird to say finding out some function is pathological or not.
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
$endgroup$
add a comment |
$begingroup$
You can think pathological as counterintuitive. Like everywhere continuous but nowhere differentiable function, uncountalbe null set, banach-tarski paradox. And it's not the rigorous concept, so it's weird to say finding out some function is pathological or not.
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
$endgroup$
add a comment |
$begingroup$
You can think pathological as counterintuitive. Like everywhere continuous but nowhere differentiable function, uncountalbe null set, banach-tarski paradox. And it's not the rigorous concept, so it's weird to say finding out some function is pathological or not.
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
$endgroup$
You can think pathological as counterintuitive. Like everywhere continuous but nowhere differentiable function, uncountalbe null set, banach-tarski paradox. And it's not the rigorous concept, so it's weird to say finding out some function is pathological or not.
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
answered Dec 7 '18 at 9:07
Lee.HWLee.HW
1137
1137
add a comment |
add a comment |
1
$begingroup$
"pathological" is a somewhat vague name for a function that gives counterexamples to incorrect statements that are not so easy to refute.
$endgroup$
– Peter
Dec 7 '18 at 8:53
$begingroup$
What do you mean by a pathological function?
$endgroup$
– Falrach
Dec 7 '18 at 9:08
1
$begingroup$
Some context would be helpful, but its probably what peter wrote
$endgroup$
– klirk
Dec 7 '18 at 9:35
$begingroup$
If that is all your source text says about when mixed partial derivatives are equal, it's time to throw it away.
$endgroup$
– user21820
Dec 17 '18 at 6:29