# Is this nonsense? Notation type of quesiton

1. Aug 25, 2013

### Jbreezy

1. The problem statement, all variables and given/known data

Hi All,
I was trying to write that $I$ is unique. $I$ is my identity element.

2. Relevant equations

3. The attempt at a solution

Maybe I can write

$\exists I | I = I$
$\forall I \in G$
Except with spaces. Is this not a way?

Just trying to specify that this thing is unique.

2. Aug 25, 2013

### lurflurf

3. Aug 25, 2013

### Jbreezy

Could you say that and then just start with this assumption I = I and proceed with a proof from there?Thanks

4. Aug 25, 2013

### lurflurf

What does I=I mean? It is always true. You want to say something like there exist a unique identity or if I and I' are any two identities then I=I'.

5. Aug 25, 2013

### Jbreezy

The question tells "Given there exits a unique identity element." So I'm just trying to use this. But having a hard time saying what I want. What I was trying to say before this was $\exists ! I$ such that I = I.
But I guess....not sure how I'm trying to say this.

6. Aug 25, 2013

### lurflurf

I would say something like
$$\exists ! I \in G |(xI=Ix=x) \forall x \in G$$
or
$$(xy=yx=x) \forall x \in G \implies y=I$$

7. Aug 25, 2013

### HallsofIvy

Staff Emeritus
"I= I" is always true whether I is denoting something that is "unique" or not. For example $\frac{1}{2}= \frac{1}{2}$ even though $\frac{1}{2}= \frac{2}{4}$ as well.