Name: Anonymous 2009-10-29 1:22
You have 1/2 < a < 1 and the infinite sequence a_0, a_1, a_2 ...
with a_i = a^i.
Can you construct sets S_n, T_n such that for all i < n either a_{2i} \elem S and a_{2i+1} \elem T or a_{2i} \elem T and a_{2i+1} holds, with lim n -> \infty S_n - T_n = 0?
That is to say, the sum of the elements in S_{\infty} - the sum of the elements in T_{\infty} = 0.
with a_i = a^i.
Can you construct sets S_n, T_n such that for all i < n either a_{2i} \elem S and a_{2i+1} \elem T or a_{2i} \elem T and a_{2i+1} holds, with lim n -> \infty S_n - T_n = 0?
That is to say, the sum of the elements in S_{\infty} - the sum of the elements in T_{\infty} = 0.