[( 0 ⋅ (−1 ÷ 0) = 0 ⋅ (−0⁻) = −1 ) ∧ ( 0 ⋅ (1 ÷ 0) = 0 ⋅ (−0⁺) = 1 ) ∧ ( −1 < 1 )] ⇒ ( 0 ⋅ (−0⁻) < 0 ⋅ (−0⁺) ) ⇒ ( −0⁻ < −0⁺ )
[( (0 ⋅ (−1)) ÷ 0 = 0⁻ ÷ 0 = −1 ) ∧ ( (0 ⋅ 1) ÷ 0 = 0⁺ ÷ 0 = 1 ) ∧ ( −1 < 1 )] ⇒ ( 0⁻ ÷ 0 < 0⁺ ÷ 0 ) ⇒ ( 0⁻ < 0⁺ )
Direction of approach can be used to determine what might otherwise be indeterminate.
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)?
I guess the following quotes by
Kurt Vonnegut would be appropriate here:
"Everything is Nothing with a twist."
https://s-media-cache-ak0.pinimg.com/736x/0f/24/16/0f2416cafb8738b50ab815863360a0d0.jpg"So it goes."
