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Topic: Simple question about irrationals, with a short note in the margin. :-)
Replies: 30   Last Post: Jan 15, 2014 6:17 PM

 Messages: [ Previous | Next ]
 William Elliot Posts: 2,637 Registered: 1/8/12
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?

> This proof must be _very_ short.

Gelfand and Schneider.

> Given you've found the above quick-and-dirty 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
>
>
>
>

Date Subject Author
1/13/14 Port563
1/13/14 William Elliot
1/14/14 Port563
1/14/14 William Elliot
1/14/14 Port563
1/14/14 William Elliot
1/14/14 Port563
1/15/14 William Elliot
1/15/14 Port563
1/15/14 Port563
1/15/14 Port563
1/15/14 William Elliot
1/15/14 Port563
1/15/14 albrecht
1/15/14 Port563
1/15/14 Port563
1/15/14 Port563
1/15/14 quasi
1/15/14 Port563
1/15/14 quasi
1/15/14 Port563
1/15/14 quasi
1/15/14 quasi
1/15/14 Port563
1/15/14 quasi
1/15/14 Port563
1/15/14 quasi
1/15/14 quasi
1/15/14 Port563
1/15/14 quasi
1/15/14 quasi