Suppose there is a sequence of n things a₁, a₂, a₃, ... a_n such that:

¬a₁Ra_n   but for any i, a_iRa_i+1   (where 0 < i < n).

Show (informally or formally) that there is a sequence a_i, a_j, a_k of three things such that:

a_iRa_j   and   a_jRa_k   but   ¬a_iRa_k.