This was a very entertaining post, thank you. The equivalence of the relation to the game really changes the approach. The proof I first came up with of his cl

This was a very entertaining post, thank you. The equivalence of the relation to the game really changes the approach. The proof I first came up with of his claim about sequences with at least one 0 vs those with infinitely many 0s was very different than the adversarial one (let b be the concatenation of all finite prefixes of a, increasing in length), and proving nonexistence of the reverse relation would have been difficult in the same constructive manner. Would it be bad form to discuss his parting challenge here?