# Meaning of Sat and Asat in the Vedic context?

The Nāsadīya Sūktam is as follows:

नास॑दासी॒न्नो सदा॑सीत्त॒दानी॒म् नासी॒द्रजो॒ नो व्यो॑मा प॒रो यत् । किमाव॑रीव॒: कुह॒ कस्य॒ शर्म॒न्नंभ॒: किमा॑सी॒द्गह॑नं गभी॒रम् ॥

It tells us that there was neither existence nor non-existence. As of existence, in its full entirety, is represented by a class Ω and non existence by M. This is because anything which cannot exist, shouldn't exist as even a thought or imagination or anything even subtler than that. So in a way we can never actually define or even name a non-existent object/ entity, hence if M = {k} where k is non-existent, M is always beyond the universe of discourse though it is not empty. Then we level up even higher, saying there was nothing in Ω or M. I mean what does it even mean to talk about the absence/presence of something that doesn't even exist? This points to either of two things - 1. We need better maths than the current set theory, or 2. There are misinterpretation of words . Please clarify.

Edit As suggested in the answer it seems that the members of the class M are impossibilities of type - "negative numbers greater than zero" or more generally, m = M1*M2 where classes M1 and M2 have nothing in common so that C is basically a null set ∅. Extending this idea, we can see we need a variation of set theory that distinguishes between different null sets on the basis of how they are composed from non-empty sets.

What I am trying to say is a simple attempt to mathematically formalize the statement in the Rigveda to understand it in more concrete manner, for example the question of existence/ non-existence of a solution to an equation arises only when we pose the initial/final/boundary conditions to it. So, it means that the universe at some point was like an unconditionalized equation, with no questions of what solutions will exist (सत्) and what won't (असत्). Am I in the right direction?