From jay.kominek@colorado.edu Wed May 01 12:19:22 2002
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Date: Wed, 1 May 2002 13:19:21 -0600 (MDT)
To: lojban@yahoogroups.com
Subject: Re: [lojban] cipja'o
In-Reply-To: <191.65c92d9.2a01940a@aol.com>
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From: Jay Kominek
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On Wed, 1 May 2002 pycyn@aol.com wrote:
> Thanks; I really was unclear about the point. As for the right word, sin=
ce I
> forget the difference between irrational and transcendantal, I was happy =
with
> {nalfrinu} till now. Now, having three not obviously equivalent definiti=
ons
> of "transcendental" (just in mathematics), I am even less sure. suppose
> what fits here it the old infinite non-repeating decimal expansion -- wh=
ich
> gives a horrible definition-type lujvo (though not as bad as "neither roo=
t
> nor quotient of rationals" or "not definable by an finite number of
> rationally coefficiented equations")
An irrational number is one which cannot be expressed as p/q where p and q
are integers.
A transcendental number is one which cannot be expressed as a polynomial
with integer coefficients. All transcendental numbes are irrational.
These are much simpler definitions than trying to refer to the decimal
expansion. Further, they're correct.
See http://mathworld.wolfram.com/ for all your math information needs.
> Time for a good metaphor, which "beyond computing" just may be, though
> it clearly sets off alarms in many people's belief webs.
Whether or not you can compute a complete decimal expansion isn't terribly
interesting, in general. Describing such a number as being "beyond
computing" is describing a secondary characteristic, which doesn't even
differentiate between irrational and transcendental numbers.
> jay.kominek
> expressed in algebraic terms.>
> But this is about transcendental numbers, which, though presumably relate=
d,
> are not quite the same thing: the algebra seems OK here -- unless rationa=
l
> coefficients are required to call it algebra.
The same expression for an appropriate Lojbanic word holds, just change
fancu into namcu.
In this case, integer coefficients are needed to call it algebra.
> We don't, of course, have a word for algebra either (nor hardly any
> other branch of mathematics -- or anything else).
http://nuzban.wiw.org/wiki/?Math%20Terminology
http://nuzban.wiw.org/wiki/?Terminology
- Jay Kominek
Plus =C3=A7a change, plus c'est la m=C3=AAme chose