Question

Which of the following is the smallest negative number?
$
  {\text{A}}{\text{. }} - 1 \\
  {\text{B}}{\text{. }} - 10 \\
  {\text{C}}{\text{. 0}} \\
 $
${\text{D}}{\text{. }}$Does not exist

Answer 1

Hint- Here, we will proceed by classifying the numbers into positive integers, negative integers or zero and then we will write the smallest and the largest positive integer followed by the smallest and the largest negative integer.

Complete step-by-step answer:
An integer is a whole number (not a fraction) that can be positive, negative or zero.
The set of positive integers are the set of natural numbers i.e., the set of positive integers start from 1 up to positive infinity where the smallest positive integer is 1 and the largest positive number occurs at positive infinity (i.e., does not exist).
The set of negative integers start from -1 up to negative infinity where the largest negative integer is -1 and the smallest negative number occurs at negative infinity (i.e., does not exist).
Therefore, the smallest negative number does not exist.
Hence, option D is correct.

Note- The set of natural numbers is the same as the set of positive integers which is defined as the numbers 1,2,3,.. up to positive infinity. The set of whole numbers contains zero along with the set of natural numbers i.e., whole numbers start from 0 up to positive infinity. In this particular problem, positive and negative infinities signify that the number does not exist.