Is 0 a rational or irrational number?

Answer 1

Rational

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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Answer 2

0 is a rational number.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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