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### IB Maths HL Option Sets Identity element

Posted: Thu Mar 07, 2013 7:39 pm
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

### Re: IB Maths HL Option Sets Identity element

Posted: Thu Mar 07, 2013 7:53 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 $x\in A$

- If an operation * admits a left-identity $e_{1}$ and a right-identity $e_{2}$, 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
$x*e=xe+4=x=>e=\frac{x-4}{x}$ which is not unique, since is depending on x. So this operation has no identity.

Hope these help