Are natural numbers CLOSED under subtraction?
AYes, because the difference of two natural numbers is always a natural number
BNo, because subtraction can give negative numbers (which are not natural)
CYes, but only sometimes
DYes, only when the larger number is subtracted from the smaller one
Answer & Solution
Correct answer: B. No, because subtraction can give negative numbers (which are not natural)
Natural numbers are {1, 2, 3, …}. The difference of two natural numbers can be 0 (e.g. 5 − 5 = 0, not in N) or negative (e.g. 3 − 5 = −2, not in N). So N is NOT closed under subtraction. This 'gap' is precisely why integers were invented — to extend N.
Related questions
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