My friend Carl Sagan recalled a Sunday long ago when at age six he had delighted in newfound counting skills. His father explained to him that there need be no end to the count. Just add one more. His father generously wrote on for the boy during the time lost to Carl's customary evening bath.
Positive integers are an infinite family whose kinship is wonderfully intricate.
Most integers can be generated by multiplying together enough smaller integers, called factors. It is called a prime number and has as factors only itself and unity. Dusan Petricic Primes are the atoms of multiplicative arithmetic. There are plenty of them, more than there are all material atoms. Euclid of Alexandria himself published a proof in the earlier part of the third century B.C. that the primes are unending.