perhaps I should apply Cantor’s Diagonal Argument to my clever construction, and of course it found a counterexample—the binary number (. . . 1111), which does not correspond to any finite whole number.
I’m not following despite having recently reviewed Cantor’s Diagonal Argument. I can imagine constructing a matrix such that the diagonal is all ones… but I don’t see how this connects up to the counterexample claim above.
Also, why worry that an infinite binary representation (of any kind) doesn’t correspond to a finite whole number? I suspect I’m missing something here. A little help please to help close this inferential distance?
I’m not following despite having recently reviewed Cantor’s Diagonal Argument. I can imagine constructing a matrix such that the diagonal is all ones… but I don’t see how this connects up to the counterexample claim above.
Also, why worry that an infinite binary representation (of any kind) doesn’t correspond to a finite whole number? I suspect I’m missing something here. A little help please to help close this inferential distance?