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Date:      Sat, 27 Jan 2001 18:27:40 -0600 (CST)
From:      Mike Meyer <mwm@mired.org>
To:        Salvo Bartolotta <bartequi@inwind.it>
Cc:        freebsd-chat@freebsd.org
Subject:   Re: OT again: Re: hexidecimal literacy
Message-ID:  <14963.26492.324702.290472@guru.mired.org>
In-Reply-To: <20010127.23473800@bartequi.ottodomain.org>
References:  <14963.8033.752142.149320@guru.mired.org> <20010127.20140200@bartequi.ottodomain.org> <14963.13797.116165.382738@guru.mired.org> <20010127.22394200@bartequi.ottodomain.org> <14963.21950.110019.468965@guru.mired.org> <20010127.23473800@bartequi.ottodomain.org>

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Salvo Bartolotta <bartequi@inwind.it> types:
> >>>>>>>>>>>>>>>>>> Original Message <<<<<<<<<<<<<<<<<<
> > Nope, only 0 is exempt. Unary is usually the first notational systems
> > ones learns for representing numbers, and is almost certainly the
> > first one discovered by humanity. It's probably used by more people
> > than binary.
> 
> I was thinking of a *positional* system of the kind a*(base raised to 
> 0) + b * (base raised to 1) + ...

Right. When base is 1, "(base raised to x)" is unity in all positions,
so it becomes the process of adding a series of 1s and 0s. Since the
position is on longer informative, you just throw it out - and the
zeros go with it. It is rather strange, but such things happen in
degenerate cases. On the other hand - those cases are part of the
beauty of the system.

> Erm, yes. Actually, I have continuous homomorphisms R -> R+  with 0 < 
> base < 1 in mind. And the contruction of the exponential functions (as 
> well as the topological theorems involved in it) IS beautiful. :-))

I tend to prefer discrete mathematics myself - I never did like the
way continuous systems feel around the edges. Yeah, I know - thats the
degenerate case for those systems.

Just to do a complete topic change, have you read:

http://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
	The Unreasonable Effectiveness of Mathematics, R.W. Hamming

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
	The Unreasonable Effectiveness of Mathematics in the Natural
	Sciences, Eugene Wigner

http://www.cfcl.com/~jef/effectiveness_mathematics.html
	Effectiveness of Mathematics, Jef Raskin

I just had them pointed out to me, but they contain things that any
mathematician - or physicist - should think about.

	<mike

--
Mike Meyer <mwm@mired.org>			http://www.mired.org/home/mwm/
Independent WWW/Perforce/FreeBSD/Unix consultant, email for more information.


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