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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
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