Are there rational numbers then irrational numbers?

Answer 1

There are infinitely many rational numbers, but there are infinitely more Irrational Numbers than rational numbers. There are more irrational numbers between 0 and 1 than there are rational numbers period.

I was kind of guessing what you were trying to ask, so let me explain some background in case that wasn't quite it. Rational numbers are those that are representable as the ratio of two integers: 2/3, 355/113, 5 (=5/1). Irrational numbers are those that cannot be represented exactly by the ratio of two integers; some familiar irrational numbers are pi and the square root of 2. There are an infinite number of integers, and therefore an infinite number of rational numbers, but the two infinities are of the same order of magnitude (called a countable or listable infinity). The mathematical designation for the kind of infinity that the integers have is called aleph-null. There are also an infinite number of irrational numbers, but it's a "bigger" kind of infinity called C or the "power of the continuum." There's a relationship between aleph-null and a larger infinity called aleph-one. It's not known whether C and aleph-one are the same or not, and if they're not, we don't know which is bigger.

Answer 2

No, there is no ordering. Some rational numbers come before irrational numbers.