How to interpret the "Omega" symbol in $\Omega_{n=0}^\infty z_n=(z_0,z_1,z_2,\ldots)$?

Question

In some notes about complex number successions i came across this symbol Ω used in this unusual way and I do not know what it means.

It would be very helpful knowing how it works.

Thanks.

Edit 1: They're notes from a complex variable class, in which the purpose it's to define the concept and some considerations about the "complex number successions". The comment on the top uses a concept between the quotation marks, in which he tries to say that the very definition of those complex number successions it's something like a"infinite ordered pair". I didn't post the full of it 'cause is in mainly in spanish.

Thanks again.

Answer 1

That is non-standard notation for an element of $\prod_{n=0}^\infty\mathbb C$. I.e., $$\Omega_{n=0}^{\infty} z_n \in \prod_{n=0}^\infty\mathbb C.$$

A more standard way to denote it would be $(z_n)_{n=0}^\infty\in\prod_{n=0}^\infty\mathbb C$.