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How to deal with the following contradiction in notation?

$\bigcup a$ may mean both:

  • the union of a collection of sets $a$;
  • $\bigcup_{i\in \operatorname{dom}a} a_i$ for an indexed family $a$ of sets.

I deal with mathematics long time, but discovered this contradictory notation only a few minutes ago.

What is the right way to deal with this?

  • 7
    As a writer: explain what your notation means before using it. As a reader: the correct interpretation is usually inferable from context.2012-03-25
  • 19
    There is no contradictory notation here. The first meaning is always intended. The second version, $\cup_{i\in x}a_i$, means *by definition*, $\bigcup A$, where $A=\{a_i\mid i\in x\}$. If $a$ is a relation, or a function, to use $\bigcup a$ to mean the second version *in your sense* is non-standard and should be frowned upon.2012-03-25
  • 4
    @AndresCaicedo: However, writing $\bigcup a_i$ as short for $\bigcup_{i \in x} a_i$ would not be uncommon, if the index set $x$ is implied by context.2012-03-25
  • 1
    I agree with Andres. Although, as Nate says, one might write $\bigcup a_i$ without making explicit the set $x$ over which $i$ ranges (if $x$ is clear from the context), I would regard the notation $\bigcup a$ (with no subscript) for this union as simply wrong.2012-12-24

2 Answers 2