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All the elements in a group must be invertible with respect to the operation. The element 0, which belongs to the set does not have an inverse wrt multiplication.

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Nabila Yousuf

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2y ago

Show that set of Irrational Numbers does not form a group w.r.t multiplication.

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Q: Why the set of rationals does not form a group wrt multiplication?
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Related questions

Does the set of even integers form a group under the operation of multiplication?

No. The inverses do not belong to the group.


Is the set of all integers a group under multiplication?

No. The set does not include inverses.


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 a set of rational numbers that begin at 0?

It could be the set denoted by Q- (the non-positive rationals) or Q+ (the non-negative rationals).


Example of group is an abelian group?

The set of integers, under addition.


What is the intersection of the rational numbers and the irrational numbers?

Some would say that there is no intersection. However, if the set of irrational numbers is considered as a group then closure requires rationals to be a proper subset of the irrationals.


What set of numbers does -23 belong to?

Integers, rationals, reals, complex numbers, etc.


What is always true about whole numbers?

They form a closed set under addition, subtraction or multiplication.


Does the set of irrational numbers with the usual addition and multiplication form a field?

Strictly speaking, no, because the identity for addition 0, and the identity for multiplication, 1 are not irrationals.


The number -4 is what set of numbers?

The number -4 belongs to the set of all integers. It also belongs to the rationals, reals, complex numbers.


Is the set of irrational numbers a group under the operation of multiplication?

No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.


What does identity property in math look like?

The identity property, of a set S and a binary operation # states that there exists, in S an element i such that for any element x is S,x # i = i # x = xIf S is the set of Integers, Rationals, Reals and the operator is addition, then the additive identity is the number 0. If the operation is multiplication, the multiplicative identity is 1.