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Is the set of all integers closed under the operation of multiplication?
Yes.
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.
How are Integers combined?
All numbers - integers as well as non-integers - are combined using different mathematical operations. Some operators are binary: that is, they combine two numbers to produce a third; some are ternary (combine 3 to produce a fourth) and so on.The set of integers is closed under some operations: common examples are addition, subtraction, multiplication, exponentiation. But not all operators are: division, for example.
Is the set of all even integers closed with respect to addition?
Yes, it is.
What is closing a rational number under addition And can you close them under subtraction multiplication and division?
Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational. To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number. For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations. 1/3 - 4/3 = -1 (remember integers are rational, too) (1/3) * (4/3) = 4/9 (1/3) / (4/3) = 1/4
What property do all nonzero numbers have that integers do not?
Of not being equal to zero. Also, of being closed under division.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Is the set of all integers closed under the operation of multiplication?
Yes.
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.
How are Integers combined?
All numbers - integers as well as non-integers - are combined using different mathematical operations. Some operators are binary: that is, they combine two numbers to produce a third; some are ternary (combine 3 to produce a fourth) and so on.The set of integers is closed under some operations: common examples are addition, subtraction, multiplication, exponentiation. But not all operators are: division, for example.
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
Why is rational numbers important?
Extending the set of all integers to included rational numbers give closure under division by non-zero integers. This allows equations such as 2x = 3 to be solved.
Is the set of all negative integers closed for operation of addition?
yes
Is the set of all even integers closed with respect to multiplication?
Yes, it is.
Is the set of all even integers closed with respect to addition?
Yes, it is.
What is closing a rational number under addition And can you close them under subtraction multiplication and division?
Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational. To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number. For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations. 1/3 - 4/3 = -1 (remember integers are rational, too) (1/3) * (4/3) = 4/9 (1/3) / (4/3) = 1/4
Why integers need extension?
In the first stage, the set of all integers needs an extension - to the set of rational numbers - to get closure for division (which is the inverse operation to multiplication).
