[penteract]

> They then proceed to compare a w1 with a 1/0 of 1:1 vs w2 with a 1:3 ratio, "skipping" 2/3 of 0s in w2, claiming a contradiction. So they're really doing a injective non-surjective mapping, not a bijective one.

There is in fact a bijection between indices that maps the sequences to each other -

  index: 0 1 2 3 4 5 6 7 ...
  w1:    1 0 1 0 1 0 1 0 ...
  w2:    1 0 0 0 1 0 0 0 ...

bijective map such that w2(f(i))=w1(i) :

  f(n) = if (n is even) then n*2 else floor((n*2+1)/3)
  f_inverse(n) = if (n is a multiple of 4) then n/2 else floor((n*3)/4)*2+1