Is 0 a rational or irrational number?

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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#.

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