Question

Why is $0$ a real number?

Answer 1

Hint: The question can be read in two ways. One will be if 0 is a Real number, here Real number means a set of negative and positive integers and fractions. The other way would be if 0 is a real number, here real number means if it is actually a number or not. Check the conditions for a Real number and a real number and then see if the number 0 fits in it.

Complete step by step solution:
Let us first consider the case where 0 is a real number.
Here we are checking if 0 is actually a number or not.
Well, zero has to be a real number, because all the numbers when considered on a vast field, whose one of the properties that it must include an element for an additive identity which states that whenever any number is added to that number, it returns the same value unchanged.
That has to be zero.
In this vast field of numbers which consists of negative and positive integers, we also need a separation point or binding point to be placed as a pivot between the negative and positive number.
That is also the task which zero does.
Hence to fulfill these and many other postulates zero “exists”.
Let us now consider where 0 is Real number.
Here Real numbers mean the set of all rational and irrational numbers.
The Real numbers follow properties such as associative property, identity property, associative property, commutative property.
Since zero follows all the given properties, it is a Real number.

Note: They are called “Real numbers” because they are not imaginary numbers and infinity is also not a real number. They can include positive numbers, negative numbers, and zero. An example of Imaginary numbers is the square root of minus 1 $\left( \sqrt{-1} \right)$