In 1928 Emanuel Sperner asked and answered the following question: Suppose we are given the set N=1,2,3,…,n. Call a family ℱ of subsets of N, which has partial order ⊆]) an antichain if no set of ℱ contains another set of the family ℱ. What is the size of a largest antichain? Clearly, the family ℱₖ of all k-sets satisfies the antichain property with |ℱₖ|=\binomnk. Looking at the maximum of the binomial coefficients (see page 14) we conclude that there is an antichain of size \binomn[n/2]= max ₖ\binomnk. Sperner's theorem now asserts that there are no larger ones.

After apologizing profusely for his errors on the first two hands, he misbid the last hand and they ended up in fifth place.

The coating contains a carbonific compound that reacts with the intumescent catalyst to form a carbon residue, and a spumific compound that decomposes to produce large quantities of gas.

The church is at grid reference 44 12.