0
$\begingroup$

Let $a=(a_1,a_2,\dots,a_n)\in [0,1]^n$, an let $B\subseteq [0,1]$. Is it common to denote the set $$ \{a_i\mid a_i\in a, a_i\in B\}$$

by $a\cap B$ ? Is there another notation?

Thanks!

$\endgroup$
0
2
$\begingroup$

Not really no. I think one would understand what you mean by $a\cap B$, but I think it should not be used.

The difference between a tuple and a set is that the tuple is ordered, but the set is not.

It means that the set

$$\{1,2,3\}$$

is equal to the set

$$\{1,3,2,2,1\}.$$

So to avoid confusions like

$$(1,2,1)\cap\{1,1,1\}={?}$$

you should not use $a\cap B$ but your other notation instead.

$\endgroup$
1
$\begingroup$

I would specifically say that using $a\cap B$ to describe the set $$ \{a_i\mid a_i\in a, a_i\in B\}$$

is an unwarranted abuse of notation that can only ever confuse the reader. I strongly advise against it.

$\endgroup$
0
$\begingroup$

One interpretation of an $n$-tuple is a function with domain $\{1, \ldots, n\}$; based on that, you could write $\mathrm{ran}\ a \cap B$. Uncouth, perhaps, but not abusive.

$\endgroup$

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.