I am unsure how the natural numbers can be identical to the p-adics. For instance, the set of natural numbers is countable, while it can easily be shown that the set of p-adics (for given p) has the cardinality of the continuum. It happens to be a firm tenet of my faith that a classic diagonal argument shows the two cardinalities cannot be the same, and it follows that the two sets cannot be the same.
Can you show me why one is wrong to follow this reasoning? Am I just another brain-washed victim of the conspiracy?
Perhaps the Atom Totality Theory can tell us something about cardinality? Does ATT refute Cantor's theory of infinite sets? Will changes in the physics of the universe influence the cardinality classes, just as they affect the values of pi and e? May the day dawn when we can prove or disprove the continuum hypothesis?