3
$\begingroup$

Assume I have 4 sets: $A$, $B$, $C$, and $D$.

What is the mathematical notation to indicate that all of these sets are pairwise disjoint?

I can obviously type:

$$A \cap B = \emptyset$$ $$A \cap C = \emptyset$$

etc.

But I am looking for a more succinct and mathematically correct way of expressing this.

$\endgroup$
  • 6
    $\begingroup$ Usually people just say "pairwise disjoint". I don't know of any standard notation for this. $\endgroup$ – ChocolateAndCheese Mar 4 '17 at 0:45
  • 2
    $\begingroup$ You could just say "The sets are pairwise disjoint". Another way is if you have sets $A_1,A_2,...,A_n$, then you could write $A_i\cap A_j=\emptyset$ when $i\neq j$ for $i,j\in\{1,...,n\}$. $\endgroup$ – Dave Mar 4 '17 at 0:47
  • $\begingroup$ Also, if the sets are non-empty and you already have a symbol for their union, say $S=A \cup B \cup C \cup D$ then you can say that the sets form a partition of $S$ $\endgroup$ – fiftyeight Jul 22 '17 at 8:07
  • $\begingroup$ Both of the suggestions above are excellent, thank you. $\endgroup$ – Kostas Jul 23 '17 at 14:13
8
$\begingroup$

If you have indexed family $\{A_i\}_{i\in I}$, then you can write $A_i\cap A_j=\emptyset$, $i\neq j$. If not, I don't see any problem in just stating: "Let $A,B,C,D$ be pairwise disjoint." This will probably be more clear than any notation you could come up with, including my own suggestion.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.