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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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