Let $S = \{1, 1/2,1/3,\dots\}$
Can we find a partition $P$ of $S$ so that each part sums to 1, e.g. $$P_1 = {1}$$
$$P_2 = { 1/2,1/5,1/7,1/10,1/14,1/70}$$
$$P_3 = {1/3,1/4,1/6,1/9,1/12,1/18}$$
$$P_4 = \{... \}$$
I think I could go on, technically, but it got increasingly complex.