The lattice of sets of natural numbers is rich. It is universal for all countable orders; it has uncountable chains isomorphic to the reals; it has uncountable antichains; yet it is highly homogeneous. https://t.co/wXdJzRSNCQ
Liouville proved the following property of the divisors of the divisors of a number: 1) Start with a number (e.g. 10) 2) Write down its divisors (1,2,5,10) 3) Write down the number of divisors of each divisor (1,2,2,4) 4) (1+2+2+4)²=81=1³+2³+2³+4³ pic.twitter.com/6YbXLdSszC
