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What sets are closed under division?
For example:* The set of real numbers, excluding zero * The set of rational numbers, excluding zero * The set of complex numbers, excluding zero You can also come up with other sets, for example: * The set {1} * The set of all powers of 2, with an integer exponent, so {... 1/8, 1/4, 1/2, 1, 2, 4, 8, 16, ...}
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)
Are the set of positive fractions closed under division?
Yes, because for any x and y that are positive fractions (y not equal to zero), x/y is also a positive fraction. Note that whole numbers are considered fractions with denominators of 1 -- otherwise it doesn't work.
Which of the following is an example of why irrational numbers are not closed under addition?
Don't know about the "following" but any irrational added to its additive inverse is 0, which is rational. Therefore, the set of irrationals is not closed under addition.
Is irrational numbers closed under division?
Nope. Quick example: e (2.71828) is irrational. Therefore 2*e is irrational making both of them elements of the set of irrational numbers. However, dividing the two, e/(2*e), gives you 1/2, which is a rational number.
Can you find a set of numbers that is closed under division and answer why?
-1, 1 is a set of numbers that is closed under division. The rule is if you divide among you end up with a quotient that is in the set. 1/-1 or -1/1 = -1 (-1 is in the set)
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.
Which set is closed under the given operation 1 integers under division 2 negative integers under subtraction 3 odd integers under multiplication?
1 No. 2 No. 3 Yes.
Is the number one 1 closed under division?
Yes
What sets are closed under division?
For example:* The set of real numbers, excluding zero * The set of rational numbers, excluding zero * The set of complex numbers, excluding zero You can also come up with other sets, for example: * The set {1} * The set of all powers of 2, with an integer exponent, so {... 1/8, 1/4, 1/2, 1, 2, 4, 8, 16, ...}
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.
What set is not closed under addition?
The set of all odd numbers. 1+1=2
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)
What operations is the set -1 0 1 closed to A Addition B Division C Multiplication D Subtraction?
Multiplication.
Give ten examples of natural number are closed under subtraction and division?
You can give hundreds of examples, but a single counterexample shows that natural numbers are NOT closed under subtraction or division. For example, 1 - 2 is NOT a natural number, and 1 / 2 is NOT a natural number.
Is whole numbers are closed under division?
No, whole numbers are not closed under division. It is possible to divide one whole number by another whole number and get a result which is not a whole number, for example, 1/2. One divided by two is a half.
Why is the set of -1 0 and 1 closed under multiplication?
Because the product of any two elements is also an element of the set.
