Can I use an index for just one ordered pair?

Question

If I have just one pair in a set, can I still index it with the number $1$, such as this set:

$\Omega = \{(\omega_1,\mu_1)\}$

or keep it as $\Omega = \{(\omega,\mu)\}$

I sort of need the indexing for a later proof of a theorem, e.g., the structure of the set $\Omega$ will change.

Thanks,

Answer 1

There's certainly nothing wrong with that, especially if it makes things more consistent later.

You could even go more general like $\Omega = \{(\omega_i,\mu_i)\}_{i \in \{1\}}$ or $\Omega = \{(\omega_i,\mu_i) : i = 1\}$ if you want to extend it to an arbitrary indexing set later.