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Re: Simple question about irrationals, with a short note in the margin. :)
Posted:
Jan 13, 2014 10:39 PM


On Tue, 14 Jan 2014, Port563 wrote:
> CAN AN ALGEBRAIC IRRATIONAL RAISED TO (the power of) AN ALGEBRAIC IRRATIONAL > (not necessarily the same one) BE RATIONAL?
> Prove the answer. > This proof must be _very_ short.
Gelfand and Schneider.
> Given you've found the above quickanddirty technique, what are the answers > to these: > STOP YOUR RUDE SHOUTING; REST IGNORED.
> > CAN AN ALGEBRAIC IRRATIONAL RAISED TO AN ALGEBRAIC IRRATIONAL BE RATIONAL? > > CAN AN ALGEBRAIC IRRATIONAL RAISED TO AN ALGEBRAIC IRRATIONAL BE > TRANSCENDENTAL? > > CAN AN ALGEBRAIC IRRATIONAL RAISED TO A TRANSCENDENTAL BE AN ALGEBRAIC > IRRATIONAL? > > CAN AN ALGEBRAIC IRRATIONAL RAISED TO A TRANSCENDENTAL BE RATIONAL? > > CAN A TRANSCENDENTAL RAISED TO AN ALGEBRAIC IRRATIONAL BE AN ALGEBRAIC > IRRATIONAL? > > CAN A TRANSCENDENTAL RAISED TO AN ALGEBRAIC IRRATIONAL BE RATIONAL? > > CAN A TRANSCENDENTAL RAISED TO A TRANSCENDENTAL BE AN ALGEBRAIC IRRATIONAL? > > CAN A TRANSCENDENTAL RAISED TO A TRANSCENDENTAL BE RATIONAL? > > > > Reminders: > Reals only, everywhere > Where types are alike, there's no requirement the power and base must be the > same number > Some may not be simple > Proofs welcomed > > > >



