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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

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William Elliot

Posts: 1,666
Registered: 1/8/12
Re: Simple question about irrationals, with a short note in the
margin. :-)

Posted: Jan 14, 2014 9:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wed, 15 Jan 2014, Port563 wrote:

> >> 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 a transcendental be an algebraic
> >> irrational?
> >>
> >> Can a transcendental raised to a transcendental be rational?

>
> Which, sadly, was the skeleton upon which I built the original post.
>
> I am unaware of proofs or examples to settle the above, but am also aware
> that I am decades out of date.
>
> I am relatively sure (in intuitive terms, that is) what are the answers:
>
> Can an algebraic irrational raised to a transcendental be an algebraic
> irrational? YES, FAIRLY SURE
>
> Can an algebraic irrational raised to a transcendental be rational? YES,
> FAIRLY SURE
>
> Can a transcendental raised to a transcendental be an algebraic irrational?
> YES, VERY SURE
>
> Can a transcendental raised to a transcendental be rational? YES, VERY SURE
>
> Any comments if your intuition indicates similarly or otherwise?


I'd conjecture they're are all transcendental.
Is it an open problem?



Date Subject Author
1/13/14
Read Simple question about irrationals, with a short note in the margin. :-)
Port563
1/13/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
William Elliot
1/14/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/14/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
William Elliot
1/14/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/14/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
William Elliot
1/14/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
William Elliot
1/15/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
William Elliot
1/15/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Re: Simple question about irrationals, with a short note in the
margin. :-)
albrecht
1/15/14
Read Re: Simple question about irrationals, with a short note in the margin. :-)
Port563
1/15/14
Read Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
Port563
1/15/14
Read Re: Four conjectures re transcendentals
quasi
1/15/14
Read Re: Four conjectures re transcendentals
quasi

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