Is 0 a rational or irrational number?

1 Answer
Trevor Ryan.
Apr 1, 2016

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.

Related questions
See all questions in Rational and Irrational Numbers
Impact of this question
10503 views around the world
You can reuse this answer
Creative Commons License