Why Is a Group with Identical Elements Considered Unfaithful?

[LagrangeEuler]

If I have some group representation $D(e)=1$, $D(s)=1$ where $e\neq s$ it is called unfaithfull because it is not isomorphism.
If I denote this group by $(\{1,1\},\cdot)$. My question is how I treat this set as a two element one, when I have only one element in the set? I'm a bit confused with this.

 

[Office_Shredder]

It's not a two element set. The group only has one element, which is the identity. The point is that D(e) = D(s).