Why can we be sure that the collection of whole numbers never ends?

Class 6Whole NumbersWhole Numbers

ABecause 0 has no predecessor
BBecause every whole number has a successor, which is again a whole number
CBecause whole numbers are closed under subtraction
DBecause 1 is the multiplicative identity

Step-by-Step Solution

Pick any whole number, add 1, and you get a larger whole number. Since this can be repeated for ever, the collection has no last member. The fact that 0 has no predecessor tells us where the list STARTS, not that it is endless, and whole numbers are not closed under subtraction at all.

Answer: B) Because every whole number has a successor, which is again a whole number

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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