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Math Duality Puzzle

Tri-Dualism Puzzle

Mathematical Lateral Thinking Puzzle... sort of...

This puzzle is intended to help remove the root assumptions upon which other facts are dependent on in order to remain true. By thinking about the possibility of something other than what we've been spoon-fed since childhood, we can then reactivate our imaginations to all of the possibilities we never even considered. 

For example, when you were young, someone introduced you to the concept of bad and good. Our whole society globally is constructed on various laws, guidelines, protocols, and so on, that have shaped and steered our brains to perform calculations based on those principles. But the truth, the actual truth that needs neither justification nor opposing force to balance it, may or may not be aligned with what we have decided must be true if all the other things we learned afterwards were to remain true.

On a Tangent...

And in that explanation is a puzzle in itself. Suppose someone does disprove duality? Does that mean there is no good or bad, heaven or hell, up or down? Not at all; what it means is that we have the opportunity to explore alternate avenues of mental processing and fact finding with our imaginations being the only limitations. With everybody on a lifelong race to find something that hasn't been done yet, why not consider the "what if" of the very thread holding our ideas of in tact was a string instead of yarn, then what you grow up to create in your mind as the limits and rules are bent, broken, rewritten, transcended, reconfigured, added, inverted, who knows? 

Now, all that is not to say you should throw away manners and composure as soon as that deadbolt secures your privacy, but we all enjoy privacy, and we all agree on that; so there you have one truth, all living beings need at least some fraction of independence as well as interdependence. That doesn't necessarily imply anything other than just that; it is not license for declarations of independence from the other inhabitants of this planet we are all entitled to equally. That is not license for dependencies to be carefully crafted and manipulated so that at the end of the day the most valuable and necessary are the cheapest, require continual support and labor, are only available to those who possess certain paper with ink that only they can make and dispense while the most useless are sold as forms of jewelry to be adorned only by the most prestigious. On every other planet, diamonds, rubies, pearls, pretty much all hardened rocks are crushed down into ultra-fine powder and evenly distributed to all living being, regardless of species, as trace nutrients to ensure the fragile circle of life continues for another generation.

IGNORE...

(GrammarQuizTN: Find 3 mistakes and Defend 3 Grammar Rules)

Let's Digress[H2]
Some philosophers have postulated throughout history (restrictive, no comma)that all actions are selfish, even those deemed selfless; my opinion is that we all need our privacy, no matter how little, but we also need each other, though that can sometimes be too much. We need each other more than we need our privacy, but(open form, we don't put a comma after but, but we could, which would be closed form.) without privacy, even the tiniest amount, we couldn't coexist. So we are dependent and interdependent of each other, collectively(Appositive). Irregardless, the pattern that has emerged and dominated is self-serve, sucker others into needing paper 'the paper makers' provide so that we can trade the necessities we slave over for the garbage 'the paper makers' convince us is worth more paper than the food and clothing we work to create, then when we trade our paper from making food, clothing, and shelter for garbage wrapped in more garbage, we will somehow be able to continue surviving by trading our garbage for the paperlessers' hard work, labor, and abuse. The below puzzle is about something else.
...TO HERE
And that seems to be all any intelligent person has ever bothered to do, what's in the best interest of their own happiness up until the end. Philosophers argue that all actions are selfish, even those deemed selfless; again, more dualism forced as the constructs upon which our understandings must be rooted from. 

So, below is a mathematical puzzle. The object of the puzzle is not to provide an answer; the puzzle is not a question in need of an answer. If you approach the below puzzle assuming you'll figure out the right answer and eliminate the wrong answers, then you're back to dualism before you even begin. There is no right or wrong, and there may or may not be an answer; those are all irrelevant. In some ways, this resembles a millennium puzzle, the handful of unsolvable math problems that defy our mathematical assumptions accepted globally by virtue of their existence, except it is not. It's simply something to help rejuvenate your imagination.

A Math Puzzle on Duality

Given three variables: Aye | One | Zeta

Zeta = Aye + One

Aye > 0

One > 0

Zeta > 0

One >< Aye (cannot be equal)

If Aye > One, Then Aye rises, and One drops

If One > Aye, Then One rises, and Aye drops

Aye is dependent on One.

As One loses, Aye gains proportionally.

As Aye gains, One loses proportionally.

One is dependent on Aye.

As Aye loses, One gains proportionally.

As One gains, Aye loses proportionally.

Zeta is dependent on both One and Aye, but not necessarily equivalently.

If Aye is greater than One, then Zeta becomes more dependent on Aye.

If One is greater than Aye, then Zeta becomes more dependent on One.

Is it possible or impossible?

if
One and Aye can never each be zero and together they can never be equal to each other,
then
zeta = one + aye
can never be as simple as zeta (1) = aye (.5) + one (.5)
and
can never be as simple as zeta (1) = aye (1) + one (0) = OR = aye (0) + one (1)

and
then
if
one is dependent on aye and zeta dependent on both

then
for example (the vice versa applies equally - pun intended)
as aye increases and one decreases
then

if
zeta shifts dependency to aye
then
aye depends more on one
and
one disappears (approaches zero)
which
cannot happen
OR
if
zeta shifts dependency to one
then
aye must reverse it dependency
causing
the reverse of the previous if (before the OR - 7 lines up)
which
cannot happen

So I guess this problem either doesn't exist or isn't solvable, but I'd love someone else's opinion besides my own

And if this has any validity, then it also might debunk dualism and all knowledge based  on dualism, which is essentially everything.

Without Zeta

Without Zeta, One and Aye cannot exist, because neither can be zero, neither can equal each other, and therefore, neither can ever approach zero as the other approaches 100%, because then it implies that one of them will eventually exist without the other.



Therefore, Zeta must be included so that One and Aye can exist, and therefore, duality is disproved.

ETA: 12/24/2025

Tri-Dualism Puzzle

Mathematical Lateral Thinking Puzzle... sort of...

This puzzle is intended to help remove the root assumptions upon which other facts are dependent on in order to remain true. By thinking about the possibility of something other than what we've been spoon-fed since childhood, we can then reactivate our imaginations to all of the possibilities we never even considered. 

For example, when you were young, someone introduced you to the concept of bad and good. Our whole society globally is constructed on various laws, guidelines, protocols, and so on, that have shaped and steered our brains to perform calculations based on those principles. But the truth, the actual truth that needs neither justification nor opposing force to balance it, may or may not be aligned with what we have decided must be true if all the other things we learned afterwards were to remain true.

On a Tangent...

And in that explanation is a puzzle in itself. Suppose someone does disprove duality? Does that mean there is no good or bad, heaven or hell, up or down? Not at all; what it means is that we have the opportunity to explore alternate avenues of mental processing and fact finding with our imaginations being the only limitations. With everybody on a lifelong race to find something that hasn't been done yet, why not consider the "what if" of the very thread holding our ideas of in tact was a string instead of yarn, then what you grow up to create in your mind as the limits and rules are bent, broken, rewritten, transcended, reconfigured, added, inverted, who knows? 

Now, all that is not to say you should throw away manners and composure as soon as that deadbolt secures your privacy, but we all enjoy privacy, and we all agree on that; so there you have one truth, all living beings need at least some fraction of independence as well as interdependence. That doesn't necessarily imply anything other than just that; it is not license for declarations of independence from the other inhabitants of this planet we are all entitled to equally. That is not license for dependencies to be carefully crafted and manipulated so that at the end of the day the most valuable and necessary are the cheapest, require continual support and labor, are only available to those who possess certain paper with ink that only they can make and dispense while the most useless are sold as forms of jewelry to be adorned only by the most prestigious. On every other planet, diamonds, rubies, pearls, pretty much all hardened rocks are crushed down into ultra-fine powder and evenly distributed to all living being, regardless of species, as trace nutrients to ensure the fragile circle of life continues for another generation.

IGNORE...

(GrammarQuizTN: Find 3 mistakes and Defend 3 Grammar Rules)

Let's Digress[H2]
Some philosophers have postulated throughout history (restrictive, no comma)that all actions are selfish, even those deemed selfless; my opinion is that we all need our privacy, no matter how little, but we also need each other, though that can sometimes be too much. We need each other more than we need our privacy, but(open form, we don't put a comma after but, but we could, which would be closed form.) without privacy, even the tiniest amount, we couldn't coexist. So we are dependent and interdependent of each other, collectively(Appositive). Irregardless, the pattern that has emerged and dominated is self-serve, sucker others into needing paper 'the paper makers' provide so that we can trade the necessities we slave over for the garbage 'the paper makers' convince us is worth more paper than the food and clothing we work to create, then when we trade our paper from making food, clothing, and shelter for garbage wrapped in more garbage, we will somehow be able to continue surviving by trading our garbage for the paperlessers' hard work, labor, and abuse. The below puzzle is about something else.
...TO HERE
And that seems to be all any intelligent person has ever bothered to do, what's in the best interest of their own happiness up until the end. Philosophers argue that all actions are selfish, even those deemed selfless; again, more dualism forced as the constructs upon which our understandings must be rooted from. 

So, below is a mathematical puzzle. The object of the puzzle is not to provide an answer; the puzzle is not a question in need of an answer. If you approach the below puzzle assuming you'll figure out the right answer and eliminate the wrong answers, then you're back to dualism before you even begin. There is no right or wrong, and there may or may not be an answer; those are all irrelevant. In some ways, this resembles a millennium puzzle, the handful of unsolvable math problems that defy our mathematical assumptions accepted globally by virtue of their existence, except it is not. It's simply something to help rejuvenate your imagination.

A Math Puzzle on Duality

Given three variables: Aye | One | Zeta

Zeta = Aye + One

Aye > 0

One > 0

Zeta > 0

One >< Aye (cannot be equal)

If Aye > One, Then Aye rises, and One drops

If One > Aye, Then One rises, and Aye drops

Aye is dependent on One.

As One loses, Aye gains proportionally.

As Aye gains, One loses proportionally.

One is dependent on Aye.

As Aye loses, One gains proportionally.

As One gains, Aye loses proportionally.

Zeta is dependent on both One and Aye, but not necessarily equivalently.

If Aye is greater than One, then Zeta becomes more dependent on Aye.

If One is greater than Aye, then Zeta becomes more dependent on One.

Is it possible or impossible?

if
One and Aye can never each be zero and together they can never be equal to each other,
then
zeta = one + aye
can never be as simple as zeta (1) = aye (.5) + one (.5)
and
can never be as simple as zeta (1) = aye (1) + one (0) = OR = aye (0) + one (1)

and
then
if
one is dependent on aye and zeta dependent on both

then
for example (the vice versa applies equally - pun intended)
as aye increases and one decreases
then

if
zeta shifts dependency to aye
then
aye depends more on one
and
one disappears (approaches zero)
which
cannot happen
OR
if
zeta shifts dependency to one
then
aye must reverse it dependency
causing
the reverse of the previous if (before the OR - 7 lines up)
which
cannot happen

So I guess this problem either doesn't exist or isn't solvable, but I'd love someone else's opinion besides my own

And if this has any validity, then it also might debunk dualism and all knowledge based  on dualism, which is essentially everything.

Without Zeta

Without Zeta, One and Aye cannot exist, because neither can be zero, neither can equal each other, and therefore, neither can ever approach zero as the other approaches 100%, because then it implies that one of them will eventually exist without the other.



Therefore, Zeta must be included so that One and Aye can exist, and therefore, duality is disproved.

ETA: 12/24/2025