# Rational Numbers Set Countable

### Points to the right are certain, and points to one side are negative.

Rational numbers set countable. Then there exists a bijection from \$\mathbb{n}\$ to \$[0, 1]\$. Suppose that \$[0, 1]\$ is countable. On the other hand, the set of real numbers is uncountable, and there are uncountably many sets of integers.

Prove that the set of rational numbers is countably infinite for each n n from mathematic 100 at national research institute for mathematics and computer science So if the set of tuples of integers is coun. It is possible to count the positive rational numbers.

The rationals are a densely ordered set: The set of positive rational numbers is countably infinite. For each positive integer i, let a i be the set of rational numbers with denominator equaltoi.

The set of all computer programs in a given programming language (de ned as a nite sequence of \legal Clearly \$[0, 1]\$ is not a finite set, so we are assuming that \$[0, 1]\$ is countably infinite. It is well known that the set for rational numbers is countable.

This is useful because despite the fact that r itself is a large set (it is uncountable), there is a countable subset of it that is \close to everything, at least according to the usual topology. Any point on hold is a real number: See below for a possible approach.

The set of all rational numbers in the interval (0;1). However, it is a surprising fact that \(\mathbb{q}\) is countable. Thus the irrational numbers in [0,1] must be uncountable.