Reading some notes on point-set topology I saw the notation $A\triangle B$ in one exercise, without any explanation of what the notation means. In this case $A$ and $B$ are sets. To provide the full context, the exercise was:
Let $X$ be a finite set, show that
$$d(A,B)= \# A\triangle B$$
is a metric.
In that case, is the notation $A\triangle B$ somehow standard? If it is, what this notation means?
3 Answers
$A\Delta B$ is the symmetric difference of the sets $A$ and $B$, the set of elements that are in exactly one of $A$ and $B$. It is also equal to $(A\cup B)\setminus (A\cap B)$.
So $\#(A\Delta B)$ is the cardinality of the set $A\Delta B$, since the ground set is finite, this is just an integer.
$A\Delta B = (A \cap \bar{B}) \cup (\bar{A} \cap B)$
edit: Which is the same as CoS answer, but written differently.
The picture depicts the "symmetric difference $A \triangle B$" of two set A and B.
