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Is the set of all integers closed under the operation of multiplication?
Yes.
Are all composite integers under multiplication?
No, not all composite integers are under multiplication. A composite integer is defined as a positive integer that has at least one positive divisor other than one and itself, meaning it has more than two factors. While all composite integers can be multiplied together, they are not inherently "under multiplication" in a mathematical sense; rather, they can simply be multiplied like any other integers.
Is the group of all real numbers except 0 under multiplication is an infinite group?
s
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.
Why integers need an 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).
Is the set of all integers closed under the operation of multiplication?
Yes.
Are all composite integers under multiplication?
No, not all composite integers are under multiplication. A composite integer is defined as a positive integer that has at least one positive divisor other than one and itself, meaning it has more than two factors. While all composite integers can be multiplied together, they are not inherently "under multiplication" in a mathematical sense; rather, they can simply be multiplied like any other integers.
Is the set of all negative integers a group under addition?
no
Is the group of all real numbers except 0 under multiplication is an infinite group?
s
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
Is the set of all even integers closed with respect to multiplication?
Yes, it is.
Show that the set of integers with respect to multiplication is not a group?
To be a group, the set of integers with multiplication has to satisfy certain axioms: - Associativity: for all integers x,y and z: x(yz) = (xy)z - Identity element: there exists some integer e such that for all integers x: ex=xe=x - Inverse elements: for every integer x, there exists an integer y such that xy=yx=e, where e is the identity element The associativity is satisfied and 1 is clearly the identity element, however no integer other than 1 has an inverse as in the integers xy = 1 implies x=y=1
Which set is closed under the operation multiplication?
Any set where the result of the multiplication of any two members of the set is also a member of the set. Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
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.
Why integers need an 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).
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).
What are the five integer rules?
I am not at all sure that there are any rules that apply to integers in isolation. Any rules that exist are in the context of binary operations like addition or multiplication of integers.
