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Why do the natural numbers need an extension?
While natural numbers are closed with respect to addition and mulitplication, they are missing the additive identity (zero). Furthermore, they are not closed with respect to two of the fundamental operations of arithmetic: subtraction and division.
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
What operations are irrational numbers closed under?
None.
Is natural numbers are closed under multipication?
IS natural numbers are closed under multiplication? Please answer as soon as possible. Thank You!
Are whole numbers closed under the operations of multiplication?
Yes.
Is Natural numbers are closed under multiplication?
Yes.natural numbers are closed under multiplication.It means when the operation is done with natural numbers in multiplication the sum of two numbers is always the natural number.
What binary operations have closure?
Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.
Why subtraction and division operations are not closed under the set of natural numbers?
2 - 8 = -6 -6 is not a natural number. 2/8 = 1/4 1/4 is not a natural number.
Are natural numbers closed under division?
No. Closed means that you could do the operation (division) on any two natural numbers and you would get a result in the natural numbers. Take 7/3 for example, this is obviously not a natural number.
Are natural numbers closed under addition?
Yes, because naturals are counting numbers, {1,2,3...} and any natural number added by another natural number has to be a natural. Think of a number line, and your adding the natural numbers. The sum has to be natural, so yes it is closed.
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
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.
