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Q: In the set of rational numbers what is the identity element for multiplication?

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For addition, 0 and for multiplication, 1.

1

I believe it is because 0 does not have an inverse element.

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.

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.

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.

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).

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

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.

A rational number is not. But the set of ALL rational numbers is.

The additive identity for rational, real or complex numbers is 0.

That is because 1 is the identity element of numbers with respect to multiplication.

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.

The additive identity for rational numbers is 0. It is the only rational number such that, for any rational number x, x + 0 = 0 + x = x

Yes. The multiplicative identity for the rational numbers is 1 (also can be written as 1/1).

No. The set of rational numbers is closed under addition (and multiplication).

Yes.

Yes, they are.

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

It the combination is multiplication and the rational number is 0, then the result is rational. Otherwise it is irrational.

Yes. Multiplication of integers, of rational numbers, of real numbers, and even of complex numbers, is both commutative and associative.

For any set of numbers, with the normal operation of multiplication defined on the set, there is only one identity, and that is 1.

yes

Yes, it is.