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Re: Re: Re: algebraic numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106236] Re: [mg106220] Re: [mg106192] Re: algebraic numbers
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 6 Jan 2010 05:57:02 -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>

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


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