Re: Re: algebraic numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg106313] Re: [mg106295] Re: algebraic numbers*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 8 Jan 2010 04:14:48 -0500 (EST)*References*: <200912290620.BAA02732@smc.vnet.net> <hhpl0g$9l1$1@smc.vnet.net> <201001050647.BAA24123@smc.vnet.net> <E44EA2F2-1274-43E8-93DE-DC5BD31884A5@mimuw.edu.pl> <op.u52ai6jwtgfoz2@bobbys-imac.local> <504E0A05-61DB-4A43-9637-68216076623C@mimuw.edu.pl> <hi1qit$etn$1@smc.vnet.net> <201001070733.CAA24037@smc.vnet.net>

Richard Fateman wrote: > Andrzej Kozlowski wrote: >> [...] > Can Mathematica represent Reals that are NOT RATIONAL? Sure. Here are > examples: Sqrt[2], 3*Pi, 4*E. 3*E +4*E^E + 5*E^E^E. > Incidentally, it is not known if E+Pi is rational. It is known whether this thread is rational. Empirical evidence seems to argue against it. > [...] > Maybe you think that Mathematica has a human mind? Of course she does. > (A better example would be 1.25, since 1.2 is not representable exactly > in binary. This example of 1.2 actually reveals a "misfeature of > mathematica. > > 1.2==5404319552844595/4503599627370496 > True. > > So 1.2 is actually Mathematica-equal to another rational number. Many, > in fact. > ) That (a misfeature), or maybe it's a missing feature in some other programs. I rather like this behavior of Equal, though I agree there is good sense behind some recent criticisms to the effect that maybe it should be configurable (regarding bits of slop, or relative or absolute error specifications). > [...] > the explanation is that Mathematica takes numbers written with a decimal > point and labels them "Real". This has nothing to do with their values, > which are, most assuredly, equal to rational numbers. And in > particular, 1.2==12/10 in Mathematica should trouble you if you believe > Mathematica speaks meaningfully on these issues. I would be far more troubled if 1.2===12/10 gave True (that is, they were deemed SameQ rather than just Equal). Much of the town is shut down, including schools (though, alas, not the HS drama club trip). I had to shovel out this morning before work. I'll have to shovel again when I get home. So here I am, and it feels like I am still shovelling. Such sound and fury... Daniel Lichtblau Wolfram Research

**References**:**Re: Re: algebraic numbers***From:*DrMajorBob <btreat1@austin.rr.com>

**Re: algebraic numbers***From:*Richard Fateman <fateman@cs.berkeley.edu>