Quote from: VectorChief on February 03, 2015, 04:54:29 PM

. . .

I see. It's getting trickier down the road, as we are probably approaching some existential paradox here.

Singularity (one zero) leads to things being undefined (division by zero).
Duality (two zeroes) necessitates trinity (three zeroes) with neutral balance point between the two, or otherwise addition lacks commutativity (-1+1 != +1-1).

Maybe those "interdimensional" modifiers provide a way out of this, because placing two zeroes (or three for that matter) on a single numerical line would always necessitate something in between: (a+b)/2.

The way I look at Earth's numerical system (according to how you describe it) is more like a pair of gears or maybe even spirals placed next to each other, rather than a single numerical line. Maybe this approach doesn't require addition to be commutative, because the time arrow is always forward and every moment in existence is unique (see my signature) so there is no way to get the same perspective (number) by following two different paths (order of addition)?

. . .

Quote from: Stover, Christopher. Limit. From MathWorldA Wolfram Web Resource, created by Eric W. Weisstein. Inc. link=http://mathworld.wolfram.com/Limit.html

Limits may be taken from below

(3)

or from above

(4)

if the two are equal, then "the" limit is said to exist

(5)

Code:

(−0⁺ + −0⁻) ÷ 2 = (⅟₀ + ⁻⅟₀) ÷ 2 = ⁽¹⁻¹⁾⁄₂₍₀₎ = −0⁺ ÷ 0 = −0⁺

Code:

(1 + 1) ÷ 2 = 2⁻ ÷ 2 = 1⁺

Code:

[( 1 + (−1 − 1) = 1 + −2 = 1 − 2 = −1⁺ ) ∧ ( (−1 − 1) + 1 = −2 + 1 = −1⁻ )] ⇒ [( 3 + (1 − 2) = (3 + 1) − 2 = 4⁻ − 2 = 2⁺ ) ∧ ( 3 + (−2 + 1) = (3 + (−2)) + 1 = (3 − 2) + 1 = 1⁺ + 1 = 2⁺ )] ⇒ ( 3 + (1 − 2) = 3 + (−2 + 1) ) ⇒ ( 1 − 2 = −2 + 1 ) ⇒ ( −1⁺ = −1⁻ )

Your existential paradox (VectorChief) arises from the notion that hyperrealitys nothing (here, nought) and everything (here, zero) exist (Stover) (i.e., are elements of the real).