You only get to ask one question per post. Since you didn't bother to specify what question you want to answer about irrational numbers, I'll just pick one at random.
Question: Which has the greater cardinality, the irrational numbers or the rational numbers?
In number theory, three facts have been proven.
1. The real numbers are uncountable.
2. The irrational numbers are uncountable
3. The rational numbers are countable.
Since the union of the countable rationals and the uncountable irrationals is the uncountable reals, the cardinality of the irrationals must be greater than the cardinality of the rationals.
John
My calculator said it, I believe it, that settles it
