Question

Is 0 a rational or irrational number?

Answer 1

Rational

Explanation:

Rational numbers `QQ` are basically all your fractions in that they can be written as a ratio of integers `ZZ`.
By definition, `QQ={m/n|m,n in ZZ, n!=0}`

Now `0` can be written as `0/n` for all `n in ZZ, n!=0`, and hence `0 in QQ`.

Irrational numbers `I` cannot be written in this form as a ratio of integers and include numbers such as `pi,e,1/sqrt2, ln2,` etc.
By definition `I=RR-QQ`, where `RR=(-oo,oo)` is the set of all real numbers.
But the set of rational and irrational numbers are disjoint, ie. they have empty intersection, and `RR` is a topological space.
In other words `I uu QQ = RR and I nn QQ = phi`.