1. Evaluate lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even.
2. Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2.
3. let r>0 and S={x in R^3:(x1)^2+(x2)^2+(x3)^2<(r)^2} show that diam S=2r.
4. let x=(x1,...xn) in Rn.show that (? k=1,n xk)^2<=n|x|^2.