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MathGroup Archive 2005

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Re: Re: Types in Mathematica thread


>>
>> 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.


But there is no reason at all to think that this would  help in  
deducing that Pi is transcendental form the fact that E is. The fact  
that neither Lindemann's nor Hilbert could do this using this ancient  
formula of Euler, which they certainly new, would make most people  
hesitate in claiming that it should be done once you have got complex  
numbers "as a prerequisite".

But if you really have an idea how to deduce that Pi is  
transcendental from the fact that E is then perhaps you might wish to  
prove that E+Pi is transcendental because somehow nobody has so far  
been able to do it.

Andrzej Kozlowski


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