Neighbourhood of an irrational
Could someone point me towards any proof for whether or not the neighbourhood around an irrational number is rational? Would the rational numbers being a dense subset of the real numbers cause there to be a rational arbitrarily close to any irrational?
Re: Neighbourhood of an irrational
Neighborhoods are neither rational nor irrational.
Originally Posted by svanbeek
Do you mean that any neighborhood of an irrational contains a rational?
The answer to that is yes. The rationals are dense in the reals.