continuous derivatives of all orders on $mathbb{R}$
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Prove that there is exists a function $fin C^infty(mathbb{R})$ such that $f(x)=0$ for $xleq 0$ and $f(x)>0$ for $x>0$.
I know that there exists many examples. But have no idea, how to prove the existence such a function.
integration sequences-and-series functions
asked Nov 16 at 14:06
HindShah
74
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show 1 more comment
up vote
-3
down vote
favorite
Prove that there is exists a function $fin C^infty(mathbb{R})$ such that $f(x)=0$ for $xleq 0$ and $f(x)>0$ for $x>0$.
I know that there exists many examples. But have no idea, how to prove the existence such a function.
integration sequences-and-series functions
asked Nov 16 at 14:06
HindShah
74
See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
I know that there exists many examples. But have no idea, how to show that such a function exists.What have I just read?
– freakish
Nov 16 at 14:14
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
1
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23
|
show 1 more comment
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
Prove that there is exists a function $fin C^infty(mathbb{R})$ such that $f(x)=0$ for $xleq 0$ and $f(x)>0$ for $x>0$.
I know that there exists many examples. But have no idea, how to prove the existence such a function.
integration sequences-and-series functions
asked Nov 16 at 14:06
HindShah
74
Prove that there is exists a function $fin C^infty(mathbb{R})$ such that $f(x)=0$ for $xleq 0$ and $f(x)>0$ for $x>0$.
I know that there exists many examples. But have no idea, how to prove the existence such a function.
integration sequences-and-series functions
integration sequences-and-series functions
asked Nov 16 at 14:06
HindShah
74
asked Nov 16 at 14:06
HindShah
74
edited Nov 16 at 14:25
asked Nov 16 at 14:06
HindShah
74
asked Nov 16 at 14:06
HindShah
74
asked Nov 16 at 14:06
HindShah
74
74
See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
I know that there exists many examples. But have no idea, how to show that such a function exists.What have I just read?
– freakish
Nov 16 at 14:14
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
1
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23
|
show 1 more comment
See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
I know that there exists many examples. But have no idea, how to show that such a function exists.What have I just read?
– freakish
Nov 16 at 14:14
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
1
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23
See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
I know that there exists many examples. But have no idea, how to show that such a function exists. What have I just read?– freakish
Nov 16 at 14:14
I know that there exists many examples. But have no idea, how to show that such a function exists. What have I just read?– freakish
Nov 16 at 14:14
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
1
1
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23
|
show 1 more comment
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See en.wikipedia.org/wiki/Bump_function.
– gj255
Nov 16 at 14:12
I know that there exists many examples. But have no idea, how to show that such a function exists.What have I just read?– freakish
Nov 16 at 14:14
@freakish The OP means that he is aware of the existence of many examples, but is not acquainted with any of them, and does not know how to produce one.
– saulspatz
Nov 16 at 14:19
1
See en.wikipedia.org/wiki/Non-analytic_smooth_function. The first example is one that you want.
– edm
Nov 16 at 14:20
@freakish Well, that's what the statement seems to mean to me. I guess it's possible that he knows of a purported example, but can't demonstrate that it satisfies the conditions, but then I feel certain he'd have told us what the function is.
– saulspatz
Nov 16 at 14:23