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. -- The Mathematica Wiki: http://www.mathematica-users.org/ Math for Comp Sci http://www.ifi.unizh.ch/math/bmwcs/master.html Math for the WWW: http://www.w3.org/Math/

**Follow-Ups**:**Re: Re: Types in Mathematica thread***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: Types in Mathematica thread***From:*Kristen W Carlson <carlsonkw@gmail.com>

**Re: Re: Types in Mathematica thread***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: Re: Types in Mathematica thread***From:*Kristen W Carlson <carlsonkw@Gmail.com>