Heilbronn set
In mathematics, a Heilbronn set is an infinite set S of natural numbers for which every real number can be arbitrarily closely approximated by a fraction whose denominator is in S. For any given real number θ {\displaystyle \theta } and natural number h {\displaystyle h} , it is easy to find the integer g {\displaystyle g} such that g / h {\displaystyle g/h} is closest to θ {\displaystyle \theta } . For example, for the real number π {\displaystyle \pi } and h = 100 {\displaystyle h=100} we have g = 314 {\displaystyle g=314} .