Nothingness cancels itself out through nothingness as negation through negation.
Considering the nature of nothingness is one of inversion of unity in multiplicity, as strict nothingness does not exist:
1) The observation of nothingness is an observation of relation through parts.
2) This relation of parts, as inverted from unity into multiplicity, observes the relation of these parts as negative boundaries in the respect the parts are seperate. In these respects negativity, as absence, is an observation of relation where one part is deficient in another because of their perceivable separateness.
3) The observation of nothingness canceling itself out through the relation of negatives negating negatives, effectively observes: The negatives, existing through nothingness, canceling out to nothing with this nothingness, as the premise for the negatives canceling itself out into unity of being in the respect that the negatives were a result of nothingness.
Now the canceling of a negative such as -1 + -1 (or -1-1) is not really a cancelation as -1 and -1 are effectively unifying as existing (albeit negative) entities in themselves. The canceling out of a negative through -1 - -1 may be more of accurate way of putting it where the negatives result in nothing.
So in one respect, and I will have to address this on a seperate thread:
1) Two negatives cancel themselves out into nothingness with this nothingness being an inversion of pure being where 0 exists as 1 in the respect it represents a point of inversion and not a thing in itself (we see this with 0 on the number line being a point of inversion between positive and negative values).
2) Two negatives result in further negatives, and the unification of negatives results in further negatives.
3) Negatives exist dually through negative and positive relations, hence the negation of a negative may result in "nothingness" (but considering "nothingness" is merely an inversion of pure being it results in "indefiniteness" or "infinity" which exists as 1 in itself.)
This negation, through division, of nothingess can be argued as simultaneously resulting in both 1 and infinity as the same time in different respects where the act of division itself, observe in 0/0...is "one infinity"...and in these respects the qualitative nature of functions are in themselves quantifiable.
Discuss...