Question

State whether the following statement is true or false.
The smallest integer is zero.
(a) True
(b) False

Answer 1

Hint: Firstly, we should know about different kinds of numbers. We will define what real numbers, whole numbers, natural numbers, decimal numbers, rational numbers and integers are. We will then see how the number in integers are arranged so that we can find its least value and check if it is 0 or not.

Complete answer:
To know about integers, we should know about the number system. The number system is like a collection of boxes in which one is kept inside another. First, there is a big box which is a collection of all kinds of numbers, they are real numbers. Real numbers are the largest set of numbers, it varies from negative infinity to positive infinity.
After real numbers, we have rational numbers. Rational numbers are the numbers of the form \[\dfrac{p}{q}\] where q is not equal to 0. They also vary over a wide range.
The numbers that start from 0 and go in a positive direction like 0, 1, 2, 3, 4…. and so on are called whole numbers.
The numbers that start from 1 and go on in a positive direction like 1, 2, 3, 4….. and so on are called natural numbers.
Then we have numbers which are not the perfect natural numbers like 1, 2.3, 3.4…but they have decimal points like 4.2, 5.7, etc. they are called decimal numbers.
Then we have numbers which are moving in both positive and negative directions. They do not consist of any fractions. For example 1, 2, 0, – 1, – 2, – 3 and so on.
Now we are asked to find the least integer. Now, as we see from the definition of integers that it moves in both directions. So, we can see that after 0, we have – 1, so clearly – 1 < 0 means – 1 is less than 0 and after – 1 we have – 2 such that – 2 < – 1.
So, we understand that 0 is not the smallest integer there are many more that are lower than 0.

Hence, the right answer is (b).

Note:
To decide which one is the least we should have good information about all kinds of numbers in place of the integer one could be confused with whole numbers. For whole numbers, the smallest digit is 0 so while answering be clear with the question.