I can't quite understand what is the set of elements you're defining your operation on, or how it is defined...
I don't know whether or not I am right about and , where being an operation on . Please tell me.
Suppose that I am correct, then I may say: Since it is a Group, it is a binary operation as well.
Suppose that the group is under multiplication.
Then on . I constructed the group table below. Please verify whether it's correct.
Since , it follows that is the identity of .
Yes?
I don't quite understand the question. Do you mean --uh--I don't even know how to put it into words?
Well, I think is under multiplication on where
I made up this question myself after I saw
on , and I want to know what is, a group or not a group?
I really don't know what I am doing because I don't have enough reading material.
Your operation has to be defined for every . What you're suggesting is not a binary operation - rather a function , .
A binary operation can be looked at as a function
.
For example, the binary operation in the example you saw, can be looked at as
Another example for a binary operation: Take and define .