Every integer is also a what. Option (A) a natural number, option
(B) a real number.
In this question, we need to
determine which of two different types of numbers is applicable to every
integer. We can start by recalling that the
integers means all of the whole numbers. That is the set of all the positive
whole numbers such as one, two, three, and so on, all of the negative whole numbers
such as negative one, negative two, negative three, and so on, and also zero. Similarly, we can recall that the
natural numbers are the set of nonnegative whole numbers, so they are the numbers
zero, one, two, three, and so on.
It is worth noting that some texts
do not include zero as a natural number; however, this will not affect the
question. We can see that negative one is a
whole number, so it is an integer. However, it is not a positive whole
number or zero, so negative one is not a natural number. Since we have found an integer that
is not a natural number, we can see that option (A) is incorrect since every integer
is not necessarily a natural number.
We can follow a similar process for
option (B). We start by recalling that the set
of real numbers is the union of the set of rational numbers and irrational
numbers. We can also recall that the set of
rational numbers is the set of all quotients of integers, that is, any number of the
form 𝑎 over 𝑏, where 𝑎 and 𝑏 are integers and 𝑏 is nonzero.
We can use this definition to show
that all integers are rational numbers. We know that dividing any integer
by one will not affect its value, so all integers can be written as the quotient of
two integers with a denominator of one. Thus, all integers are rational
Since the set of real numbers
includes all rational numbers, we can say that the set of integers is a subset of
the set of rational numbers, which in turn is a subset of the set of real
numbers. This means that all integers are
rational numbers and that they are also all real numbers, which is option (B).