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MathGroup Archive 2005

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Re: Types in Mathematica thread

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62891] Re: Types in Mathematica thread
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Thu, 8 Dec 2005 00:04:17 -0500 (EST)
  • References: <dmp9na$hi2$1@smc.vnet.net> <roadnYOk3NcFDw7eRVn-jg@speakeasy.net> <200512050837.DAA08425@smc.vnet.net> <200512051840.NAA21063@smc.vnet.net> <200512060503.AAA02736@smc.vnet.net> <dn3jsl$8s0$1@smc.vnet.net> <5_ydnSmM8KqB-gjenZ2dnUVZ_v6dnZ2d@speakeasy.net> <dn5npi$nef$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej Kozlowski wrote:

> 
> On 6 Dec 2005, at 19:25, Steven T. Hatton wrote:
> 
> 
> 
>>>
>>> Well, actually the proofs for E and Pi are quite different.
>>
>> I believe you can derive Pi from E, so it should be possible to
>> prove the
>> former from the latter.
> 
> 
> I have decided to give up discussing computer science issues (see
> last remark at the  bottom) but this is a different matter. "Derive
> Pi form E"? What on earth can you mean? Are you by any chance
> referring to something like the Euler formula:
> 
> Exp[I Pi]==-1.

Yes.

> In that case would you say that you can also "derive" I form Pi and
> E? What do you mean by deriving a number from another number? 

I meant to say that Pi can be defined in terms of E.  I am assuming the
definition of complex numbers as a prerequisite.  It's something that's
been in the back of my mind for quite some time. 

> Hm. Are you aware of the following:
> 
> 1. There is no known algorithm that can determine if a given
> algebraic number is real or not.
> 2. Consider these simple examples:
> 
> IntegerQ[Cos[Pi/7]^2+Sin[Pi/7]^2]
> 
> False
> 
> and also try this:
> 
> Element[1 + I*(Cos[Pi/7]^2 + Sin[Pi/7]^2 - 1), Reals]

Not @ Element[1 + I*(Cos[Pi/7]^2 + Sin[Pi/7]^2 - 1), Complexes]

> Do you still claim that
> 
>> Thus RealQ might
>> test for everything that is a number, and not Complex.

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