# Algebraic numbers dense in R

How would I show that the algebraic numbers are dense in R. I know that the rationals and irrationals are dense in R.

• @Alti: You’re making this much too hard. A set $D$ is dense in $\Bbb R$ if every open interval $(a,b)$ contains a member of $D$. The rationals are dense, so every open interval contains a rational, and therefore automatically contains an algebraic number. Therefore? – Brian M. Scott Oct 1 '12 at 6:38