Does specifying two elements in a set imply they are not the same element?

Question

Pretty basic question regarding set theory notation;

Suppose I have a set $A$. If I then write $a,b\in A$, does that automatically imply $a\neq b$ due to the fact I've used two separate dummy variables? Is it possible to have $a=b$ even if the value of $a=b$ is unique in $A$?

Thanks

Answer 1

No, writing $a, b \in A$ does not imply that $a \not= b$. You definitely need to say that $a$ and $b$ are distinct elements if you want to have this property.