Why Is a Group with Identical Elements Considered Unfaithful?

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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.
 
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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).
 

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