Posted: Sep 14, 2015 6:00 pm
crank wrote:
scott1328 wrote:
crank wrote: I had difficulties with some bad arguments I tried to counter

crank wrote:with some wrong assumptions on my part, and other issues.

this is true

crank wrote: Chaitin's claim, if I understand it, is that reals are infinite precision,

That wasn't his claim.
crank wrote:but that isn't a mathematical term, so whatever, since uncomputable numbers will have an infinite, non-repeating decimal representation, they in effect contain infinite information,

uncomputable numbers have no decimal representation whatsoever, if they did, they would be computable. Uncomputables contain no information whatsoever.

You got one right. Uncomputables have decimal representation, you can't right one out, but you can begin to generate one, in principal, the easiest would be a random number generator [not the computer algorithmic ones, true random number generators].

Chaitin:
But when you work on a computer, the last thing on earth you're ever going to see is a real number, because a real number has an infinite number of digits of precision,

Chaitin was clearly speaking in the context of computing real numbers. He was not making the claim you have put into his mouth.

But to say you can begin writing an uncomputable number out is false because all you have done with your random number generator is generate a number that equally identifies countably infinite rational number, countably infinite computable numbers, and uncountably infinite non-computable numbers.

In what sense of the word have you identified any number whatsoever with your random number generator?