Question

Can real numbers be negative?

Answer 1

Hint: Here in this question, we have to classify the real numbers means we have to discuss the topic of what is real numbers or definition of real number, what are all the different types of numbers including in it or set of real numbers and Examples of real numbers.

Complete step by step answer:
Now, Real numbers is a set of all positive and negative numbers that contains the Subsets of Integers, Rational and Irrational numbers.
All numbers of the form $\dfrac{p}{q}$, $q \ne 0$ are rational numbers and any number of the form $\dfrac{p}{q}$, $q = 0$ is an irrational number because with $0$ as denominator the number cannot be defined.
Now Integers as we know are all positive or negative rational numbers, of the form $\dfrac{p}{q}$, $q = \pm 1$.
Thus, we can conclude that integers are a special case of real numbers, so integers belong to the set of real numbers only.
Therefore, we can say that real numbers can be negative.

Note:
All integers are real numbers but all real numbers are not integers. A real number can always be expressed in the form $\dfrac{p}{q}$, $q \ne 0$ if it is a rational number, whether positive or negative. For example, $5$ is a real number which is a rational number as it can be written as $\dfrac{5}{1}$. Similarly, $ - \dfrac{4}{5}$ is also a rational number and a real number. However, the number $\dfrac{3}{0}$ is not a rational number as the denominator is $0$.But, it is a real number as real numbers contain both rational and irrational numbers.