 The next special element that might exist in a set that I want to talk to you about very quickly is just the inverse element the inverse element In this element Let's just have a look at that. So again, we're going to have a set of elements x. We're going to have a binary Operate operation on that. Let's make it that and we have to have a unique an identity element So there must be an identity element here My identity element. We're just going to make that U Just that identity element and now I'm going to have Two elements in that set x sub 1 and x sub 2 they are elements of my set And I'm going to say I'm going to define again as human beings. We define it this way We decided that x 2 is an inverse element of x 1 if the following holds So x 2 is an inverse element of the following if the following holds That if I take this binary operation That is going to equal this basically but that equals The important bit is that this equals the Back to the identity element A nice example a very easy example if we just take the set our set to be The rational the rational numbers Let's say that my element that i'm looking at x 1 is 3 what would be under my binary operation being multiplication Multiplication What would it be? Well, if that is 3 then this is going to be a third because 3 times a third equals 1 And we defined 1 under this for this set Under this binary operation We define this as the identity element which we have there So that is our definition of an inverse element