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IB Mathematics HL Option: Sets, Relations and groups (Identity element)

Has the binary operation on R defined be x*y=xy+4 an identity element?

Thanks

Has the binary operation on R defined be x*y=xy+4 an identity element?

Thanks

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

IB Mathematics HL Option Sets, relations and Groups - Identity element

The basic principles about identity element are:

- An element e in a set A is an identity element for an operation * defined over A if

e*x=x*e=x for every element

- If an operation * admits a left-identity and a right-identity , then these two identities are equal.

- If a binary operation * on a set A admits an identity element e, then this element is unique.

Concerning your question, suppose that the identity element is e, then

which is not unique, since is depending on x. So this operation has no identity.

Hope these help

The basic principles about identity element are:

- An element e in a set A is an identity element for an operation * defined over A if

e*x=x*e=x for every element

- If an operation * admits a left-identity and a right-identity , then these two identities are equal.

- If a binary operation * on a set A admits an identity element e, then this element is unique.

Concerning your question, suppose that the identity element is e, then

which is not unique, since is depending on x. So this operation has no identity.

Hope these help

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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