Which are more? Rational numbers or irrational numbers?

[CALCULUS' GOD]

Which are more?
(A) rational numbers or (B)Irrational numbers.

 

[stapel]

Which are more?
(A) rational numbers or (B)Irrational numbers.

There are infinitely-many of each, and there are loads of proofs and discussions regarding the fact that the "size" of the "infinity" of irrationals is "larger" than the "infinity" of rationals. (For instance, here.)

So what, really, is your question? Please be specific. Thank you!

 

[lookagain]

The answer here is that there are in fact far, far more irrational numbers than there are rational numbers. One way to think about this is that between any two rational numbers, there are an infinite number of irrational numbers. ... Any set that has cardinality is said to be countably infinite.

Why respond to a five-year-old thread!? Is what you claim a sufficient reason for the set
of irrational numbers having a larger cardinality than the set of rational numbers?
Is your reasoning complete? What about if you choose any two irrational numbers?
Can you tell me that you won't always be able to get an infinite number of
rational numbers between them?

 

[pka]

The answer here is that there are in fact far, far more irrational numbers than there are rational numbers. One way to think about this is that between any two rational numbers, there are an infinite number of irrational numbers. ...

Before one really says that consider this; Between any two irrational numbers there is a rational number.

 

[Steven G]

The integers is said to be countably infinite just like the rationals, Hmm, aren't there an infinite number of rationals between any two consecutive integers. So the integers and rationals have different cardinalities? I need to remember forget that one!

 

[pka]

The integers is said to be countably infinite just like the rationals, Hmm, aren't there an infinite number of rationals between any two consecutive integers. So the integers and rationals have different cardinalities? I need to remember forget that one!

Every non-integer \(J\) then \((\exists K\in\mathbb{Z})[K<J<K+1]\)