Talk:Small set (combinatorics)

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Why does the divergence of the harmonic series imply the converse of the Erdos-Turan conjecture? In fact, isn't the converse false?

Thinking about the issue briefly, consider the subset of the series

(1)+(1/2+1/3)+(1/4+1/5+1/6)+(1/8+1/9+1/10+1/11)+(1/16+1/17+1/18+1/19+1/20)

i.e.

\sum_{i=0}^\infty \sum_{j=0}^i 1/(2^i+j)

whose reciprocals contain arbitrarily long arithmetic progressions (an arithmetic progression of length n and common difference 1 starts after 1/2^n). But this series converges, bounding above by \sum n/2^n (which converges by the integral test).

So the comment on the converse seems to be in error; any thoughts?

Agreed. The page is in error, and should be corrected. 67.191.231.108 23:37, 21 August 2007 (UTC)