In the Number System (Class 9 Math Chapter 1), students often face True/False statements regarding the classification of numbers. One of the most common statements is: 'Every natural number is a whole number.'
Natural Numbers (N): Start at 1. (1, 2, 3...).
Whole Numbers (W): Start at 0. (0, 1, 2, 3...).
N is a subset of W.
The only difference between the two sets is the number ZERO (0).
Statement: Every natural number is a whole number. Answer: TRUE.
To understand why, let's look at the sets of numbers:
Natural Numbers (N): These are counting numbers starting from 1.
Whole Numbers (W): These are all the natural numbers, plus zero.
If you look closely, the entire set of Natural numbers is sitting directly inside the set of Whole numbers. Therefore, every single natural number is also a whole number.
Statement: Every whole number is a natural number. Answer: FALSE. Reason: The number 0 is a whole number, but it is NOT a natural number. Therefore, the reverse statement is false.
Yes, it is True. Since the set of whole numbers (0, 1, 2, 3...) contains all the natural numbers (1, 2, 3...), every natural number is also a whole number.
No, 0 is a whole number and an integer, but it is not a natural (counting) number.
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