A recessive trait is often depicted as a lowercase letter, while a dominant trait is depicted as a capital letter. So, aa has two recessive genes, AA has two dominant genes, and Aa has both a dominant and a recessive gene. To eliminate the recessive gene, it has to have less of a chance of survival than the dominant gene. After a lot of time, if the aa or Aa gene keeps mixing with either AA or Aa genes, eventually the recessive gene will go away, although it will take many generations.