# What is the convention for listing an uncountable series of elements"

If I have an uncountable series of elements $$x_j$$, what is the convention for listing them? It doesn't correct to write: $$\{x_1, x_2, x_3, \ldots \}$$ since that implies they can be indexed by $$\mathbb{N}$$. Maybe we don't list uncountable elements but that makes telling a story about them hard. (I couldn't find a better tag, sorry if notation is misleading.)

• If you have your uncountable indexing set $I$, and the elements are called $a_i$, then one fairly standard way is $\{a_i\}_{i\in I}$ Jan 16 at 2:06
• @Lubin, thanks - does the job nicely. Jan 16 at 6:30

The standard way of indexing is as follows: given set $$A$$ and indexing set $$I$$, such that there is a bijection $$i\mapsto x_i$$ that maps each $$i\in I$$ to some $$x_i\in A$$, we write $$\{x_i\}_{i\in I}$$
There's actually no reason to "index" an uncountable set this way. Any time you feel the urge to write something like $$\bigcup_{i\in I}x_i$$where $$I$$ is an uncountable index set and $$S=(x_i)_{i\in I}$$ you can simply write $$\bigcup_{x\in S}x$$instead.