Re:How can some infinities be bigger than others?
by ginnungagap on Thursday April 20, 2023 @06:16AM
(#35638121)
What are those trivially defined {r0,r1} for the "interleaving digits" map f:(0,1) -> (0,1)^2 defined by taking a real x in (0,1), writing its decimal expansion as
x=0.a1a2a3a4a5a6...
(always pick the nonrepeating decimal expansion in case x has two) and sending it to the pair (y,z) where
y=0.a1a3a5...
z=0.a2a4a6...
(Using (0,1) is no issue since we can compose later with bijections (0,1) -> R)
Edit: I'm not sure why I cannot reply to your reply, but {π,π} is not even in (0,1)^2
x=0.a1a2a3a4a5a6...
(always pick the nonrepeating decimal expansion in case x has two) and sending it to the pair (y,z) where
y=0.a1a3a5... z=0.a2a4a6...
(Using (0,1) is no issue since we can compose later with bijections (0,1) -> R)
Edit: I'm not sure why I cannot reply to your reply, but {π,π} is not even in (0,1)^2