Originally Posted by

**chinglu**
Yes, well, you cannot use Peano-Dedekind theory for set theory based on the 2 incompleteness theorems of Godel unless you can prove the Diagonal Lemma is flawed. More specifically, according to Cantor's theorem, in contrast to his so called diagonal theorem, the power set under ZFC of the natural numbers produces a cardinality greater than that of the model N that satisifies Peano-Dedekind.

I warn casual readers that almost all of this is complete gibberish.

1. The Peano axioms, sometimes referred to as the Peano-Dedekind axioms, are just that - axioms. Things that seem reasonable to all reasonable Men. There exists no "theory" called Peano-Dedekind;

2. The claim that "you cannot use the Peano-Dedekind

**axioms** for set theory unless the diagonal lemma is flawed" is totally without meaning. There exists NO "diagonal lemma";

3. The proof that the cardinality of the powerset on the natural numbers

is strictly greater than that of

is just an application of the diagonal

** argument **of Cantor.

4. Using this fact, it is possible to demonstrate (albeit rather non-rigorously) the first incompleteness Theorem of Goedel. So this post is sort of on it's head. And that from the world's greatest logician!

As usual, chinglu appears to post content he fails to understand. Worse, he fails to understand that some members here

*do* understand it