| Computers Forum Index » Computer - Games Programming (Algorithms) » [OT] integral name... |
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| Leclerc... |
 Posted: Fri Jul 24, 2009 12:35 am |
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Guest
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Hi,
AFAIK, I think the following integral has a name, but I can't recall it:
int frrm 0 to 1 f(x)*dx,
where f(x) == 1 if x is rational, and f(x) == 0 otherwise
thanks,
Gordan |
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| Miles Bader... |
| Posted: Sun Sep 06, 2009 5:16 am |
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Leclerc <gordan.sikic.remove at (no spam) this.inet.hr> writes:
Quote: int frrm 0 to 1 f(x)*dx,
where f(x) == 1 if x is rational, and f(x) == 0 otherwise
Eek, sorry I dunno the name, but... that's a pretty freaky concept!!
-miles
--
Occam's razor split hairs so well, I bought the whole argument! |
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| David Lamb... |
| Posted: Tue Sep 08, 2009 4:06 am |
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Miles Bader wrote:
Quote: Leclerc <gordan.sikic.remove at (no spam) this.inet.hr> writes:
int frrm 0 to 1 f(x)*dx,
where f(x) == 1 if x is rational, and f(x) == 0 otherwise
Eek, sorry I dunno the name, but... that's a pretty freaky concept!!
Missed the OP, but... not every function is integrable, and I really
wonder if something as discontinous as that qualifies. |
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| Lacrymology... |
| Posted: Tue Sep 08, 2009 2:41 pm |
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Quote: Missed the OP, but... not every function is integrable, and I really
wonder if something as discontinous as that qualifies.
Thatīs not integrable by normal means, but there's an extension for
integrals which allows to integrate functions that are discontinuous
"for almost every point" (that's the term it was explained to me with,
and that was exactly the function used). I don't remember the result,
tho.. |
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| Paul E. Black... |
| Posted: Tue Sep 08, 2009 8:25 pm |
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Guest
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On Saturday 05 September 2009 22:23, Miles Bader wrote:
Quote: Leclerc <gordan.sikic.remove at (no spam) this.inet.hr> writes:
int frrm 0 to 1 f(x)*dx,
where f(x) == 1 if x is rational, and f(x) == 0 otherwise
Eek, sorry I dunno the name, but... that's a pretty freaky concept!!
I believe that the integral is 0: there just aren't enough rational
numbers.
-paul-
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Paul E. Black (p.black at (no spam) acm.org) |
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| Lacrymology... |
| Posted: Wed Sep 09, 2009 2:40 pm |
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Guest
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The function is called The Dirichlet Function, the integration for
nowhere-continuous functions is called the Lebesque Integral, and the
integral is indeed 0. Wikipedia and Google FTW |
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