Re: Re: Re: algebraic numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg106237] Re: [mg106220] Re: [mg106192] Re: algebraic numbers*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Wed, 6 Jan 2010 05:57:14 -0500 (EST)*References*: <200912290620.BAA02732@smc.vnet.net> <hhpl0g$9l1$1@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

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