Question

The collection of all whole numbers less than $10$. Does the above statement represent a set? Justify.

Answer 1

A collection of well-defined elements is known as a set and It won’t change from elements to elements. It is always denoted by a capital letter and listed within the flower braces. Elements in the sets don’t need to be in order, but the elements are not allowed to repeat. For example, a set of all-natural numbers is a set and it is denoted by N.

Complete step-by-step solution:
It is given that the collection of all whole numbers is less than $10$.
First, let us create this set and name it.
We know that the whole numbers are $0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...$.
We need whole numbers less than $10$, let us collect them. The whole numbers that are less than $10$ are $0,1,2,3,4,5,6,7,8,9$.
Let us put them in a curly brace $\\{ 0,1,2,3,4,5,6,7,8,9\\}$.
We know that the set name should be denoted by a capital letter so, let us denote it as A.
Therefore, A $= \\{ 0,1,2,3,4,5,6,7,8,9\\}$.
Now let us verify whether it is a set or not. Set A is a set since it has a finite number of elements so it is finite and also it is well-defined. Also, we can see that no element is repeated.
Thus, set A $= \\{ 0,1,2,3,4,5,6,7,8,9\\}$ is a set, that is, the collection of all numbers less than $10$ is a set.

Note: We know that a set is a well-defined collection of elements. There are many types of sets some of them are singleton set which contains only one element, empty set which contains no elements, finite set which contain a definite number of elements, an infinite set is a set that is not finite, etcThe collection of all whole numbers less than $10$ is a finite set.