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Earn +20 ptsQ: Is the set of natural numbers closed under addition?
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Why are natural numbers not under addition?
Natural numbers are actually closed under addition. If you add any two if them, the result will always be another natural number.
Is there a subset of the natural numbers that is closed for addition?
Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.
Which set of numbers is closed under addition?
Natural (ℕ), integer (ℤ), rational (ℚ), real (ℝ) and complex (ℂ) numbers are all closed under addition.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
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