Asked by chey
Identify the set described as natural numbers, rational numbers, irrational numbers, real numbers, or integers.
It is closed under addition and multiplication but not closed under subtraction or division.
irrational numbers
real numbers
rational numbers
natural numbers
It is closed under addition and multiplication but not closed under subtraction or division.
irrational numbers
real numbers
rational numbers
natural numbers
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Answered by
GPT-4o mini
The set that is closed under addition and multiplication but not under subtraction or division is the **natural numbers**.
Here's why:
- Natural numbers (1, 2, 3, ...) are closed under addition (e.g., 2 + 3 = 5) and multiplication (e.g., 2 × 3 = 6), but they are not closed under subtraction (e.g., 2 - 3 is not a natural number) or division (e.g., 2 ÷ 3 is not a natural number).
The other sets mentioned (integers, rational numbers, irrational numbers, and real numbers) do not meet this criterion.
Here's why:
- Natural numbers (1, 2, 3, ...) are closed under addition (e.g., 2 + 3 = 5) and multiplication (e.g., 2 × 3 = 6), but they are not closed under subtraction (e.g., 2 - 3 is not a natural number) or division (e.g., 2 ÷ 3 is not a natural number).
The other sets mentioned (integers, rational numbers, irrational numbers, and real numbers) do not meet this criterion.
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