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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: 1,484
Registered: 1/8/12
Re: Simple question about irrationals, with a short note in the
margin. :-)

Posted: Jan 15, 2014 12:19 AM
  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:

> My thinking went vaguely along these lines:
>
> (1) Almost all reals (i.e. all but countably many; there is a bijection from
> algebraic numbers to naturals) are transcendental.
>
> (2) Transcendental numbers can be approximated very closely (indeed, as
> closely as
> is possible) by algebraic numbers close to them.
>
> Algebraic numbers, however, cannot be approximated very closely (indeed, as
> closely as is possible) by algebraic numbers close to them.


If a is an algebraic numbers, then a + 1/n is an
algebraic number as close to a as you may wish.



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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