Define “sumbunol” as meaning “some but
not all”; and “nunnerol” as “none or all”. Now consider this troika:

Voter A is contemplating the equation 1x = 0. To Voter A, the equation is solved by sumbunol numbers.

Voter B is contemplating the equation 0x = 1. To Voter B, the equation is solved by no numbers.

Voter C is contemplating the equation 0x = 0. To Voter C, the equation is solved by all numbers.

So by 2/3 majorities:

Some number solves the equation.

Some number does not solve the equation.

Nunnerol numbers solve the equation.

As ever, the trilemma is a deductive engine; from any two derive the negation of the third. Thus:

From: some numbers solve, some numbers don’t solve; derive; sumbunol numbers solve.

From: some numbers don’t solve, nunnerol numbers solve; derive; no numbers solve.

From: nunnerol numbers solve, some numbers solve; derive; all numbers solve.

Voter A is contemplating the equation 1x = 0. To Voter A, the equation is solved by sumbunol numbers.

Voter B is contemplating the equation 0x = 1. To Voter B, the equation is solved by no numbers.

Voter C is contemplating the equation 0x = 0. To Voter C, the equation is solved by all numbers.

So by 2/3 majorities:

Some number solves the equation.

Some number does not solve the equation.

Nunnerol numbers solve the equation.

As ever, the trilemma is a deductive engine; from any two derive the negation of the third. Thus:

From: some numbers solve, some numbers don’t solve; derive; sumbunol numbers solve.

From: some numbers don’t solve, nunnerol numbers solve; derive; no numbers solve.

From: nunnerol numbers solve, some numbers solve; derive; all numbers solve.

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