Quote from: username18333 on January 31, 2015, 05:30:33 AM

Quote from: VectorChief on January 28, 2015, 01:42:37 AM

Also what would be the result of -1+1? Which of those inner zeroes?

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[( −1 − (−1) = −1 + 1 = −0⁻ ) ∧ ( 1 + (−1) = 1 − 1 = −0⁺ )] ⇔ [( −0 = −0⁻ ∧ −0⁺ ) ∧ ( −0⁻ < −0⁺ )]

In the first cases, one approaches nought from the positive direction. In the last cases, one approaches nought from the negative direction.

The answer to -1+1 that I held in mind was −0⁻ + −0⁺, which would not be reducible further in Earth's numerical system, but would represent zero under conventional mathematics. This makes addition commutative:

−0⁻ + −0⁺ = −0⁺ + −0⁻ = −0 <- not on the axis, but rather an imaginary bridge?

When it comes to subtraction, we get the following:

−0⁻ - −0⁺ = −0⁻ + −0⁻ = −0⁻
−0⁺ - −0⁻ = −0⁺ + −0⁺ = −0⁺

Subtracting polarized nought from non-polarized nought would destroy the bridge resulting in polarized nought of opposite sign. Adding it would be equivalent to subtracting with sign inverted. Subtracting polarized nought from itself should reestablish the bridge resulting in non-polarized nought.

This in fact adds a three-state modifier to all non-zero numbers as well, something that conventional mathematics didn't have due to its zero being singular (thus adding/subtracting it had no effect). It should look like this:

1 + −0⁻ = 1⁻
1 + −0⁺ = 1⁺
1 + −0 = 1

Which reminds me of the (past, present, future) modifiers used in conjunction with numbers in the new type of numerology (described here, scroll all the way down to Numerology).

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These interdimensional three have no energy of their own. They must have the other numbers to function. This also makes them catalytic. It also places them in a circle with the others instead of a line or a column. Some will understand this, and some will not. If you had the numbers one to nine in a column-going down a page that you were looking at, think of the other three as hovering above the column. This is the best we can do to explain something that's out of your normal 4D conception.

In your example: -1+1 = −0⁻ < −0⁺ = +1-1 => -1+1 < +1-1
Does Earth's addition commute? Is strict inequality due to implied modifiers?

PS: Also you might have mixed the terms positive and negative in your description.