Rolf, I was implicitly assuming that even knowing BB(k), it still takes O(k) bits to learn BB(k+1). But if this assumption is incorrect, then I need to change the setup of my prediction game so that the input sequence consists of the unary encodings of BB(1), BB(2), BB(4), BB(8), â¦, instead. This shouldnât affect my overall point, I think.
Rolf, I was implicitly assuming that even knowing BB(k), it still takes O(k) bits to learn BB(k+1). But if this assumption is incorrect, then I need to change the setup of my prediction game so that the input sequence consists of the unary encodings of BB(1), BB(2), BB(4), BB(8), â¦, instead. This shouldnât affect my overall point, I think.