
Re: Simple question about irrationals, with a short note in the margin. :)
Posted:
Jan 15, 2014 12:19 AM


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.

