Which is the formal mathematical notation that the following sentence can be stated?
"Let the mutually exclusive events $A_1,A_2,\ldots,A_n$"
$\begingroup$
$\endgroup$
2
-
$\begingroup$ What do you want this for? If you're writing something, "The events $A_1,\,A_2,\,\ldots,A_n$ are (pairwise) mutually exclusive" is likely clearer than any symbolic expression of the same. $\endgroup$– Milo BrandtNov 27, 2015 at 4:29
-
$\begingroup$ @MiloBrandt I was reading something and I was curious about it because I have never come across it. $\endgroup$– AdamNov 27, 2015 at 4:30
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
One way to write it is:
$\forall i, j: 1 \le i \lt j \le n \implies A_i \cap A_j = \emptyset$
(Although it seems a lot easier to understand the way you stated it!)
answered Nov 27, 2015 at 5:12
$\begingroup$
$\endgroup$
It really depends on what you want to express, do you want to describe that the events are mutually intersection free, then write it as Dan Brumleve suggests as $$ \forall i, j: 1 \le i \lt j \le n \implies A_i \cap A_j = \emptyset $$ if you want to express that the sets (events) are indeed mutually independent to some probability measure, then you might be better off with $$\forall i, j: A_i \perp_{i\neq j} A_j$$ Keep in mind, that both statements are not equivalent.
answered Nov 27, 2015 at 5:28
$\begingroup$
$\endgroup$
I have seen things like $$A_1\sqcup\dotsb\sqcup A_n$$ before. I can't say that this is universal or widely accepted though.
