Video Transcript
Is seven a rational or an
irrational number?
In this question, we are asked to
determine if seven is a rational or an irrational number. To determine this, we can start by
recalling that we call a number rational if it can be written as the quotient of two
integers, where the denominator is nonzero. If we cannot write the number in
this way, then we say that it is an irrational number. This allows us to directly answer
this question, since we know that seven is equal to seven divided by one, so it is a
rational number.
We could end the question here. However, it is worth noting that
this same reasoning can be extended to any integer. If we have an integer 𝑚, then we
can note that 𝑚 is equal to 𝑚 over one, which is the quotient of two integers. So 𝑚 must be a rational
number. This shows that all integers are
rational numbers. We can write this in set notation
by writing that the set of integers is a subset of the set of rational numbers.
