IB Maths HL Option Sets Identity element

Operation table of a group, Symmetries of plane figures, Cycle notation for permutations, Left and right cosets, group homomorphism, kernel, kernel and range of a homomorphism, isomorphisms

IB Maths HL Option Sets Identity element

Postby elizabeth » 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?

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Re: IB Maths HL Option Sets Identity element

Postby miranda » 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

- 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 :) :)
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