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Sameer writes two collections on the board: the whole numbers W = 0, 1, 2, 3, … and the natural numbers N = 1, 2, 3, …. How many numbers belong to W but NOT to N?

Class 6Whole NumbersWhole Numbers
  • A0
  • BInfinitely many
  • C1
  • D2

Step-by-Step Solution

The two lists match perfectly from 1 onwards, so the only number in W that is missing from N is 0. That is exactly 1 number. Answering "infinitely many" comes from imagining that the two lists end in different places; in fact both go on for ever.
Answer: C) 1

Key idea: Closure: when an operation 'stays inside' the whole numbers

Adding two whole numbers always gives a whole number — addition is **closed** on whole numbers. Multiplying two whole numbers always gives a whole number — multiplication is **closed** too. But subtraction is **not** closed: 5 − 7 = −2, which is not a whole number. Division is also not closed: 7 ÷ 2 = 3.5, not a whole number. Closure is the property that lets us trust an operation never to take us 'outside' the world of whole numbers.

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By how much does the smallest whole number differ from the smallest natural number?How many whole numbers have exactly two digits?Why can we be sure that the collection of whole numbers never ends?Which of these quantities can NOT always be recorded as a whole number?In the whole numbers, what can you say about the predecessor of 0?