Question

State whether the following statement is true or false.

The smallest integer is zero.

(a) True

(b) False

Answer 1

Hint: Use the fact that integers include all positive and negative whole numbers without any fractional or decimal part. Compare all the possible values of integers to find the smallest integer and check if the given statement is correct or not.

Complete step-by-step solution:

We have to check if the statement ‘The smallest integer is zero’ is correct or not. To check the validity of the given statement, we will use the definition of integers. We know that integers include all positive and negative whole numbers without any fractional or decimal part.

Integers are numbers of the form $...-3,-2,-1,0,1,2,3,...$. 

We observe that -1 is less than zero and -2 is less than -1 and so on. It means that a number is less than all the numbers that are written on its right side and greater than all the numbers written on its left side. Thus, all negative numbers are less than zero and all positive numbers are greater than zero. So, zero is not the smallest integer. However, we can say that zero is the smallest non-negative integer. Hence, the given statement is false.

Therefore, the correct answer is option (b).

Note: We must keep in mind that we have to compare 0 with all the positive and negative integers. We observe that there is no smallest integer as there are an infinite number of integers and for each integral value; we can find an integer smaller than the given integer.