Are there many more irrational numbers than rational? [duplicate]

number-theory

Yes, in the sense of cardinality. In the same sense that one can say that there are more real numbers than there are rationals (or integers; or natural numbers).

The rational numbers are countable, but the irrationals are uncountable.

Related

Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
Order of conjugate of an element given the order of its conjugate
What is the closed form of $\int e^{x^2} \, dx$?
Every subset of a subspace of $\mathbb{R}^n$ of dim $<n$ has measure 0
How to prove that $\lim_{n\rightarrow \infty}\frac {n^{2}}{2^{n}}=0$ & $\lim_{n\rightarrow \infty}\frac {n^{2}}{n!}=0$?
Inequality involving a finite sum
Can anyone confirm expectations for the game of blackjack?
Sufficient Conditions for proving $V$ is a vector space
How to prove by induction that $|\sin(nx)| \leq n|\sin x|$?
composition of the derivative of Dirac delta with a function
Show that $I(a,b)=I(a',b')$
How to use Fermat's little theorem to find $50^{50}\pmod{13}$?