Some great replies, gives me a lot to think about

Terms like "well behaived" when applied to the "functon" make me wonder what
stipulations might be implied by the language that you'd have to be a formal
mathmatician to interpret.  As an example, I don't even know what the
instrinsic properties of a "function" may be in this context.

Since it's an infinit series I suppose it doesn't really matter, given
enough time you could prove out any rational requirement? which is why you
can throw math at it.  If it was just a bunch of random numbers that started
somewhere and stopped somewhere, I doubt anyone would be writing equations
that mean anything.  I'd guess we would turn to statistics at that pint to
supply some context.

As a broad answer to questions posted in a couple of the replies, my
interest lies in imrpoving my understanding of specifically what the SNST
proves, and the requirements for it to be valid.

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