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Is the set of all multiples of a positive integer n closed under multiplication?
Wiki User
∙ 11y ago
Yes, it is.
Consider any two elements of this set, both are multiples of n, so they can be written as pn and qn for some integers p and q. Multiplying them together, we obtain pqn^2, which can be factored into (pqn)n. This result is clearly a multiple of n.
Since the product of any two multiples of n is also a multiple of n, the set of all multiples of n is closed under multiplication.
Wiki User
∙ 11y ago
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What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
True or False The set of whole numbers is closed under subtraction Why?
A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)
Is the set of integers closed under subtraction?
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.
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.
Is the set of whole numbers are closed under multiplication?
If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.
Are positive integers closed for multipication?
No, but they are closed for multiplication.
Is a positive number closed for addition and for multiplication?
yes
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
Are cubed numbers closed under multiplication?
Yes. If you have two positive integers "a" and "b", and their corresponding cubes "a^3" and "b^3" (using "^" for "power"), then the product of the two cubes would be a^3 times b^3 = (ab)^3. Since the product of "a" and "b" is also an integer, you have the cube of an integer.
Why are all the perfect squares are rational number?
A perfect square is a square of an integer.The set of integers is closed under multiplication. That means that the product of any two integer is an integer. Therefore the square of an integer is an integer.Integers are rational numbers so the square [which is an integer] is a rational number.
True or False The set of whole numbers is closed under subtraction Why?
A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)
Why is the product of positive numbers positive?
Multiplication is shorthand for repeated addition, for example 5 × 4 is the same as 5 + 5 + 5 + 5 or 4 + 4 + 4 + 4 + 4. Repeatedly adding a positive number to itself will result in a positive number.
Is the set of composite number closed under multiplication?
Is { 0, 20 } closed under multiplication
Are integers closed under division?
No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
Is 018 closed under multiplication?
No.
Are whole numbers closed for multiplication?
no
What are the fundamental operations of integers?
I am not sure there are any fundamental operations of integers. The fundamental operations of arithmetic are addition, subtraction, multiplication and division. However, the set of integers is not closed with respect to division: that is, the division of one integer by another does not necessarily result in an integer.
