Re: Re: Re: algebraic numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg106364] Re: [mg106313] Re: [mg106295] Re: algebraic numbers*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sun, 10 Jan 2010 03:31:30 -0500 (EST)*References*: <200912290620.BAA02732@smc.vnet.net> <hhpl0g$9l1$1@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

Sound, yes, but I don't think fury. Bobby On Fri, 08 Jan 2010 03:14:48 -0600, Daniel Lichtblau <danl at wolfram.com> wrote: > 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 > -- DrMajorBob at yahoo.com