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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?

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Our Set theory does not even cover indeterminates(not-a-number, like 0/0, inf/inf etc). Compare NaN Vs 0. 0 is just a symbolic representation of the 'nothingness' as applicable to Numbers( Rational, Complex, etc.). The Theory of Transfinite Numbers by George Cantor 'attempts' to extend the concept of 'infinity' to the Axiomatic Set Theory( we still assume conceptual Axioms, symbolic logic, etc.) by bijections among sets. We see the 'Continuum hypothesis', Conjectures between orders of Infinity, etc. We delve deep on those. Still, NaN is not covered. Can you extend traditional Fields (Real, Rational etc.) with NaNs? The Mathematics Fails & Set operations are not applicable or constructions for operators involving both NaN and a Number are at best, super vague. Let's come back to Nasadiya Sukta. 'There even non-existence was not'. This refers to the concept of non-existence. or e.g Non-existent number is 0. Non-existent sound is silence. Non-existent light is darkness and so on. A non-existent Space implies infinitely packed matter & so on. You can also apply non-existence to the number 0, !0 = 1, non-existence of darkness implies light, non-existence of silence is sound, etc. But these are ALL attributes of the Parahbrahman at some level. Our sentience - the consciousness blob- discovered these attributes, using thought, logic, etc. with our biology. In the case of Valakilyas and Kratus, who don't have a body but just Pure Consciousness essence, they could also have come up with the concept of existence & non-existence without the help of Biology (Pancha bhoothas). You could also have been a single-point conscious particle, that came up with these. Since we call ourselves having a 'reality'/ Waking state are we a Real Number? This I've wondered about. Are we Quaternions? with 4 states of consciousness? Jagrat, Swapna, Sushupti, Turiya states? a higher-order number? It's all very vague. What then at these levels is Non-existence? For applying Math, you need precise definitions. If Math itself is based on Axioms, Incompleteness theorems( Godel's for one), and Non-inclusive of NaN, Abstract Disk Embedding Theorems & Such in a Topological space, How can we expect to Use Set Theory to capture even more abstract concepts of Parama vyoma, Vyoma, the existence or non-existence of those? So, Yes Our Current Math is not enough to define the non-existence as a 'generalized' concept. Note that we are assuming some 'truth', some axioms EVEN to describe these. What is that? It's the truth in the meaning of the 'collection' of words that I write. or should I say, a collection of some symbols with interleaved spaces with the contemporary assignment of Meaning / Mapping to another Set ! What about the non-existence of 'That' truth itself? :-) See the Paradoxical, vague constructs evolving as you try to apply non-existence? That's why Set Theory isn't enough as it stands today!

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