Posted by: fortunefaded March 15, 2012
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I will strictly talk from the view of mathematics since it looks like that's where you are coming from...
This takes me back to when I first learned of Cantor's diagonal argument. To your question of set a and b. They both have the same size, proper mathematical term being cardinality.
But the cardinaility of real numbers is greater than natural number, which one can see because there are infinitely many real numbers within any two natural numbers.
But what used to trip me off is that the cardinality of natural numbers and rational numbers are same, even though there are infinitely many rational numbers within any 2 natural numbers. It's one of those things that I believe the diagonlization proof shows.
So there are various levels of infinity and it's interesting to think of them but few philosophers and mathematicans went crazy from it so I would try to avoid it if possible :D
FF
This takes me back to when I first learned of Cantor's diagonal argument. To your question of set a and b. They both have the same size, proper mathematical term being cardinality.
But the cardinaility of real numbers is greater than natural number, which one can see because there are infinitely many real numbers within any two natural numbers.
But what used to trip me off is that the cardinality of natural numbers and rational numbers are same, even though there are infinitely many rational numbers within any 2 natural numbers. It's one of those things that I believe the diagonlization proof shows.
So there are various levels of infinity and it's interesting to think of them but few philosophers and mathematicans went crazy from it so I would try to avoid it if possible :D
FF