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The Number System is a system for representing numbers on the Number Line using a collection of symbols and rules. These symbols, which range from 0 to 9, are referred to as digits. The Number System is used to accomplish mathematical computations ranging from complex scientific calculations to simple counting of gifts or the number of books left in the box. Numerous types of number systems exist, each with a different base value for its digits.
Natural Numbers
Numbers may be found everywhere around us, used for counting items, representing or trading money, calculating temperature, telling time, and so on. These numbers are referred to as “natural numbers” since they are used to count items. When counting items, it may be said 5 glasses, 6 books, 1 bottle, and so on. Natural numbers are sometimes referred to as counting numbers in common, especially in primary school education, to intuitively exclude negative integers and zero.
Whole Numbers
The set of whole numbers is identical to the set of natural numbers, with the exception that it includes a 0 as an extra number. In mathematics, the set of whole integers is expressed as 0, 1, 2, 3, … it can be seen from the definitions above that any natural number is a whole number. Furthermore, all whole numbers other than 0 are natural numbers.
What whole number is not a counting number?
Answer:
There is only a number that is a whole number but not a counting number. That number is 0. It’s important to note that 0 (Zero) isn’t a Natural Number. The set of whole numbers is {0, 1, 2, 3, … ∞} and the set of natural numbers or counting numbers is {1, 2, 3, … ∞}. Therefore, it is clear that 0 is not a counting number but is a whole number. Every counting starts with the number 1 and not 0 and hence, 0 shall not be included in the counting numbers.
Sample Problems
Question 1: What is another name for natural numbers?
Answer:
They are the numbers from 1, 2, 3, 4, 5, … they are referred to as natural numbers because they may be seen in nature and are hence naturally occurring. Also, Natural numbers are sometimes referred to as counting numbers to intuitively exclude negative integers and zero. They are known as counting numbers because counting starts from 1 and so are the natural numbers.
Question 2: What’s the Difference Between Natural and Whole Numbers?
Answer:
Natural numbers, such as 1, 2, 3, 4, and so on, are all positive numbers. They’re the numbers you’re used to counting, and they go on indefinitely. The entire numbers, on the other hand, are all natural numbers, including zero, such as 0, 1, 2, 3, 4, and so on. All whole numbers and their negative counterparts are considered integers. -4, -3, -2, -1, 0,1, 2, 3, 4, and so on are some examples.
Natural Numbers = {1, 2, 3, 4, 5, 6, 7, 8, 9,…}
Whole Numbers = {0, 1, 2, 3, 4, 5, 7, 8, 9,…}
Question 3: Give examples for natural numbers.
Answer:
Natural Numbers include the numbers 1, 2, 3, 4, 5, and so on. Counting is done using these numbers.
Question 4: Briefly explain the whole number with examples.
Answer:
If 0 (Zero) is included in the set of Natural Numbers, the result is a set of Whole Numbers. It indicates that the numbers 0, 1, 2, 3, 4, 5, and so on are all whole numbers.
Question 5: What are even numbers?
Answer:
Even Numbers are Natural Numbers that are divisible by two. 2, 4, 6, 8, 10, and so on.
Question 6: What are odd numbers?
Answer:
Odd Numbers are natural numbers that are not divisible by two. For instance, 1, 3, 5, 7, and so on.
Question 7: What are prime numbers?
Answer:
Prime numbers are natural numbers that are not divided by any other integer except 1 and self. 2, 3, 5, 7, 11, and so on.
Question 8: What are composite numbers?
Answer:
Composite numbers are natural numbers that are also divisible by any other integer besides 1 and self. 4, 6, 8, 9, 10, 12, and so on.
Question 9: What are integers?
Answer:
Integers are a collection of whole numbers and natural numbers that encompass negative, positive, and zero values. -2, -1, 0, 1, 2, 3 and so on.
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