# Can we represent pi as a dedeking cut in the rationals

1. Sep 6, 2011

### Khichdi lover

Hi , I only recently read the construction of reals from rationals.

I could grasp that $\sqrt{2}$ can be represented as the set of rationals given by
{x$\in$ Q : x2 < 2 } . As we know this set is defined purely in terms of Q.

Is there a dedekind cut representation for pi as well ?

I read somehwhere that not all reals can be defined. But since pi is defined , what would it's dedeking cut representation be?

2. Sep 6, 2011

3. Sep 6, 2011

### Hurkyl

Staff Emeritus