Math information representations

[master_coda]

Originally posted by Organic
No dear master_coda,

If the list is complete, then any R number must be in the list, therefore we cannot find any R number (by using Cantor's function) which is not in the list.

And we cannot find any output result (by using Cantor's function) which is not in the list, if and only if we have no input.

Question: And when we have no input?

Answer: When we have no way to represent the list.

Therefore when the R list is complete, we cannot represent it, and cannot conclude if it is uncountable XOR countable.

Without information we cannot prove anything about R numbers.

You don't even have a basic understanding of a proof by contradiction. The whole point of the a proof is that even though you can't find a real number not in the list, you can still find a real number not in the list.

When a proposition and it's negation are both true, you have a contradiction. That means that you are reasoning from a false premise. In this case, the premise is that it is possible to construct a complete list. You can't write a complete list of the reals because if you could, you could show that something is both true and false.

 

[Organic]

Dear master_coda,

It does not matter any more because i have found a way to represent a list of 2^aleph objects.

Please see my thread:

https://www.physicsforums.com/showthread.php?s=&threadid=10383



Doron Shadmi

 

[Hurkyl]

... Question: And when we have no input?

Answer: When we have no way to represent the list.

The correct answer is "When no such list exists."