The set of all prime numbers is contained within the set of rational numbers, but they are rational numbers that are not within the set of prime numbers.
Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B.
Just because you can map two infinity's to each other does not mean they are of the same size consider: Limit(0->inifinity) of (x - (x/2)) algebraically that's clearly Limit(0->inifinity) of X/2 which is infinity.
PS: What makes Cantor's diagonalization interesting is you can repeat it recursively an infinite number of times. This is more obvious in base 2.
Cantor's diagonalization is simply demonstrating that same inequality by showing a number in set A is not in set B.
Just because you can map two infinity's to each other does not mean they are of the same size consider: Limit(0->inifinity) of (x - (x/2)) algebraically that's clearly Limit(0->inifinity) of X/2 which is infinity.
PS: What makes Cantor's diagonalization interesting is you can repeat it recursively an infinite number of times. This is more obvious in base 2.