Is this a valid identity element? A dilemma

There is an operation on a set (real numbers) such that:

Does have an identity element with respect to operation ?

Now I find the identity element like this:

So now

Is this a valid identity element for this operation?

Because an identity element has a property that it doesn't change the original element when used with the operation on set .

can be The original element is modified.

But it's also possible that . The original element is left untouched. I'm confused by these two situations.

So my question is:

Is this a valid identity element of with respect to ?

Re: Is this a valid identity element? A dilemma

Quote:

Originally Posted by

**x3bnm** There is an operation on a set

(real numbers) such that:

Does

have an identity element with respect to operation

?

There is no such that .

So the answer is no.

Re: Is this a valid identity element? A dilemma

Quote:

Originally Posted by

**Plato** There is no

such that

.

So the answer is no.

Thanks Plato for answer. I didn't think of that way. Again thanks.