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From: Archpawn
Subject: Cantor's Razor
Date: 8 Oct 2012 23:25:00
Message: <web.507398f9a3f9a0033bdd455d0@news.povray.org>
People keep making razors with more and more blades. I present a razor with too
many blades to count. This set of blades is not only perfect, but closed and
totally disconnected as well.


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From: waggy
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 02:40:00
Message: <web.5073c5f48e862ba19726a3c10@news.povray.org>
"Archpawn" wrote:
> People keep making razors with more and more blades. I present a razor with too
> many blades to count. This set of blades is not only perfect, but closed and
> totally disconnected as well.

What an amusing concept!

Unfortunately my monitor does not have infinite DPI, so most of the detail seems
to be lost to anti-aliasing.


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From: Le Forgeron
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 13:04:57
Message: <50745939$1@news.povray.org>
Le 09/10/2012 08:36, waggy nous fit lire :
> "Archpawn" wrote:
>> People keep making razors with more and more blades. I present a razor with too
>> many blades to count. This set of blades is not only perfect, but closed and
>> totally disconnected as well.
> 
> What an amusing concept!
> 
> Unfortunately my monitor does not have infinite DPI, so most of the detail seems
> to be lost to anti-aliasing.
> 
> 
What about a Cantor's broom ?
It would at least be a real application of dust on dust.


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From: Archpawn
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 14:35:01
Message: <web.50746d758e862ba13bdd455d0@news.povray.org>
And now a version with a fat cantor set. What's the point of having uncountably
many blades if it still has zero measure?


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From: Christian Froeschlin
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 15:56:52
Message: <50748184$1@news.povray.org>
Archpawn wrote:

> People keep making razors with more and more blades. I present a razor with too
> many blades to count. This set of blades is not only perfect, but closed and
> totally disconnected as well.

too complicated. I'm keeping my trusted Dirichlet razor ;)


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From: Christian Froeschlin
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 16:00:07
Message: <50748247$1@news.povray.org>
Christian Froeschlin wrote:

> too complicated. I'm keeping my trusted Dirichlet razor ;)

(trying to get a hair between the blades is a form of meditation for me)


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From: Le Forgeron
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 16:44:19
Message: <50748ca3$1@news.povray.org>
Le 09/10/2012 20:31, Archpawn nous fit lire :
> And now a version with a fat cantor set. What's the point of having uncountably
> many blades if it still has zero measure?
> 

Shipping cost: weight of blades is 0, number of blades is so huge...

And the biggest point for the seller: you have one razor, you cut it in
three (or two ?) parts and now can sell one while keeping the other one
and repeat. The more you sell, the smaller the razor, but still the same
number of blades.


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From: Archpawn
Subject: Re: Cantor's Razor
Date: 9 Oct 2012 21:00:01
Message: <web.5074c8408e862ba13bdd455d0@news.povray.org>
Christian Froeschlin <chr### [at] chrfrde> wrote:
> too complicated. I'm keeping my trusted Dirichlet razor ;)

I don't know what that is. Is it related to Dirichlet series?

If you want things simple, may I suggest Occam's razor?

Le_Forgeron <jgr### [at] freefr> wrote:
> Shipping cost: weight of blades is 0, number of blades is so huge...

No. The edges have zero measure. The solid still has volume.


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From: Le Forgeron
Subject: Re: Cantor's Razor
Date: 10 Oct 2012 01:40:09
Message: <50750a39$1@news.povray.org>
Le 10/10/2012 02:58, Archpawn nous fit lire :
>> Shipping cost: weight of blades is 0, number of blades is so huge...
> 
> No. The edges have zero measure. The solid still has volume.
> 

I wonder. Finite x Finite x 0 = ?


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From: Christian Froeschlin
Subject: Re: Cantor's Razor
Date: 10 Oct 2012 17:54:02
Message: <5075ee7a@news.povray.org>
Archpawn wrote:
> Christian Froeschlin <chr### [at] chrfrde> wrote:

>> too complicated. I'm keeping my trusted Dirichlet razor ;)
> 
> I don't know what that is. Is it related to Dirichlet series?

I thought about Dirichlet function f:R->R
f(x) = {1 if x is rational number | 0 otherwise}

Put in one blade for each rational number ;)


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