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Re: Re: Re: algebraic numbers
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106238] Re: [mg106220] Re: [mg106192] Re: algebraic numbers
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Wed, 6 Jan 2010 05:57:26 -0500 (EST)
*References*: <200912290620.BAA02732@smc.vnet.net> <hhpl0g$9l1$1@smc.vnet.net> <201001050647.BAA24123@smc.vnet.net> <E44EA2F2-1274-43E8-93DE-DC5BD31884A5@mimuw.edu.pl> <op.u52ai6jwtgfoz2@bobbys-imac.local> <504E0A05-61DB-4A43-9637-68216076623C@mimuw.edu.pl> <op.u529salwtgfoz2@bobbys-imac.local> <771DE886-36BB-4108-A83C-808109BAA8C3@mimuw.edu.pl> <op.u53a91u1tgfoz2@bobbys-imac.local>
Well, I think when you are using Mathematica it is the designers of
Mathematica who decide what is rational and what is not.
And when you are not using Mathematica (or other similar software which
interprets certain computer data as numbers), than I can't imagine what
you could possibly mean by a "computer number".
Andrzej
On 6 Jan 2010, at 11:45, DrMajorBob wrote:
> Obviously, it DOES make them rational "in a sense"... the sense in
which I mean it, for example.
>
> Bobby
>
> On Tue, 05 Jan 2010 20:41:34 -0600, Andrzej Kozlowski
<akoz at mimuw.edu.pl> wrote:
>
>>
>> On 6 Jan 2010, at 11:13, DrMajorBob wrote:
>>
>>> I completely understand that Mathematica considers 1.2 Real, not
Rational... but that's a software design decision, not an objective
fact.
>>
>> I think we are talking cross purposes. You seem to believe (correct
me if I am wrong) that numbers somehow "exist". Well, I have never seen
one - and that applies equally to irrational and rationals and even
(contrary to Kronecker) integers. I do not know what the number 3 looks
like, nor what 1/3 looks like (I know how we denote them, but that's not
the sam thing). So I do not think that the notion of "computer numbers"
makes any sense and hence to say that all computer numbers are rational
also does not make sense. There are only certain things that we
interpret as numbers and when we interpret them as rationals they are
rationals and when we interpret them as non-computable reals than they
are just that.
>> Of course we know that a computer can only store a finite number of
such objects at a given time, but that fact in no sense makes them
"rational".
>>
>> Andrzej Kozlowski
>
>
> --
> DrMajorBob at yahoo.com
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