[Doctor Stochastic]

I am saying because it is not a random number, Omega cannot be in it - and neither can Shakespeare.

Then you are denying Champernowne's (and others) proof. Mathematics (and scientific endeavors in general) are not like à la carte menus, you have to take the whole thing, you cannot pick and choose which theorems you with to accept. Once the axioms are agreed, the consequence are not in dispute.

[Alamo-Girl]

Thanks for your post!

I don’t see where you are getting that I am denying axioms. I’m agreeing with you that Champernowne’s constant is not random. At post 645 you said (emphasis mine):

Then you haven't understood the significance of Champernowne (or Borel's work on which it is based.) Champernowne's construction (and some that I have invented, too) generate all possible finite bit patterns with the proper frequency. These sequences are not random, but they do satisfy the strong law of large numbers.

To which I said:

I am saying because it is not a random number, Omega cannot be in it - and neither can Shakespeare

For Lurkers, Omega is Chaitin’s random number: Randomness and Complexity in Pure Mathematics

As far as I know, Omega is the “best thing out there” for a random number – so it seems rather obvious to me that if Champernowne’s number which derives from an algorithm contains Chaitin’s Omega, then Chaitin’s claims that Omega’s bits “have no structure” could not be true. The above link discusses both Champernowne and Omega.

My objection concerning Shakespeare is different but also based on the fact that Champernowne’s number is not random (as you said.) At the bit level, the incremental spread of on/off bits is such that high order bits will stay “on” for ever increasing durations as the power of 2 increases. This creates a hard pattern – a correlation – that translates to unprintable/unreadible alphanumeric characters in an 8 bit ASCII character set.