0
In the set of rational numbers what is the identity element for multiplication?
Wiki User
∙ 14y ago
1 is the identity for multiplication.
1*x = x = x*1 for all rational x.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
What are the identity elements for the addition and multiplication of rational numbers?
For addition, 0 and for multiplication, 1.
What is the identity element of numbers for multiplication and division?
1
What is the product of a number and its inverse is 1?
That is the identity property of multiplication for all rational numbers, or all real numbers or all complex numbers except (in each case) for 0.
What do identity property of multiplication mean?
If a set, with multiplication defined over its elements has the identity property it means that there is a unique element in the set, usually denoted by i, such that for every element x in the set, x*i = x = i*x.If the elements of the set are numbers then i = 1.
What is inverse in algebra?
Given a set and a binary operation defined on the set, the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation. If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k. If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.
What are the identity elements for the addition and multiplication of rational numbers?
For addition, 0 and for multiplication, 1.
What is the identity element of numbers for multiplication and division?
1
Why are the rational numbers under the operation of multiplication not a group?
I believe it is because 0 does not have an inverse element.
What is the product of a number and its inverse is 1?
That is the identity property of multiplication for all rational numbers, or all real numbers or all complex numbers except (in each case) for 0.
What do identity property of multiplication mean?
If a set, with multiplication defined over its elements has the identity property it means that there is a unique element in the set, usually denoted by i, such that for every element x in the set, x*i = x = i*x.If the elements of the set are numbers then i = 1.
Are rational numbers closed under multiplication?
Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.
What is inverse in algebra?
Given a set and a binary operation defined on the set, the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation. If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k. If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.
0 and 1 are not prime numbers but apparently they have their own special names what are they?
They both considered "identity elements". 0 is actually the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Mathematicians refers to 0 as the additive identity (or better said, the reflexive identity of addition). 1 is a separate and special entity called 'Unity' or 'Identity element'. 1 is actually the identity element under multiplication for the real numbers, since a x 1 = 1 x a = a. Mathematicians refers to 1 as the multiplicative identity (or better said, the reflex identity of multiplication).
Why there is a need of a null vector?
It has the role of the identity element - same as, in the case of real numbers, the zero for addition, and the one for multiplication.
What is Additive identity?
The additive identity for rational, real or complex numbers is 0.
What is the identity property of multiplication and addition?
The identity property of multiplication asserts the existence of an element, denoted by 1, such that for every element x in a set (of integers, rationals, reals or complex numbers), 1*x = x*1 = x The identity property of addition asserts the existence of an element, denoted by 0, such that for every element y in a set (of integers, rationals, reals or complex numbers), 0+y = y+0 = y
What is the definition for identity property of multiplication?
The identity property for a set with the operation of multiplication defined on it is that the set contains a unique element, denoted by i, such that for every element x in the set, i * x = x = x * i The set need not consist of numbers, and the multiplication need not be the everyday kind of multiplication. Matrix multiplication is an example.
