Collatz Conjecture Unique Solution
Murgu Table2To3
which been validate multiple times by:
Murgu - Collatz Conjecture Pocket Map
Marker USA Murgu Arrow
Murgu Infinity Collatz Table2To3 Functions
AND MATHEMATIC LOGICAL BEAUTY
Infinity Marker USA Murgu Arrows
Collatz Conjecture One Dimension Array.

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Maybe first Group Theory with a final Absolute Truth Validation.

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Murgu Table2To3 or Collatz Table2To3 are Mathematic 2 Collatz Conjecture Murgu New Formulas

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((2^(2k+2)[1+6i]) - 1) = 3 Q_i
((2^(2l+1)[5+6j]) - 1) = 3 Q_j

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for k=l=0 , and if wish to see it before exploring what is down, here is a link for.
Murgu_Table2To3 - Collatz Table3To3, Click here

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For Infinity Murgu Table2To3 (above functions for k=l=0 to Infinity), where we give an small example - See :
Infinity Murgu_Table2To3 - Collatz Table3To3 , Click here

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Grids separation and new Mathematics Logic implied may can include Collatz Table2To3 into Group Theory beauty.

Murgu_Table2To3 - Collatz Table3To3

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Short Presentation

For Mathematicians, Murgu Table2To3 Formulas as double linear Functions Solved Collatz Conjecture as Unique Solution.
But strange state of proud keep it in state of continue hacking.
Collatz Conjecture was solved via all Mathematics Rigor and with absolute new methods and logical new afford. Here will expose in short every step for not in historic order, but in logic one.
1. In a logical order, can say solution started via a new Group Theory, which groped Positive Integers in Murgu Grids of 6 Integers. This Brought 6 new formulas for.
(1+6i) - (2+6i) - (3+6i) - (4+6i) - (5+6i) - (6+6i) -- G.0

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2. Then make an important new step by analyzing Collatz Conjecture Murgu Inverse Method Legacy for.
Collatz Conjecture Murgu Inverse used Collatz Conjecture first procedure, (3x + 1), write as
(3x + 1) = 2^k D_i

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Its legacy for is natural and became Collatz Conjecture Murgu Inverse Method Procedure
((2^k D_i -1)/3) = Q_i

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3. The logic fact, Collatz Conjecture Murgu Inverse Method Procedure became Odd To Odd Formulas lead to formal and temporal elimination of evens as are
2^k D_i where D Odd

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5. This natural logical fact lead to Collatz Conjecture Murgu Coordinate system.
Murgu Table2To3

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6. Murgu Lemas and analytic work lead to Murgu Table2To3 Formulas which became also Collatz Conjecture Murgu double Linear Functions.

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7. Odds distinctive proprieties legacy make My to offer formal name for
(1 + 6i) and (5 + 6i) - Logical Eternal Triads (LET's)

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(3 + 6i) - Logical Dead Nodes or Collatz Conjecture Murgu Closures (LDN)

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8. As Murgu Inverse Method Murgu Table2To3 Formulas are Down to UP Connections formulas and reveal LDN's do not have UP Connection Node , it reveal, Collatz Conjecture Murgu Table2To3 Formulas as Collatz Conjecture Functional Divergence Formulas.
((2^(2k+2)[1+6i]) - 1) = 3 Q_i     (C.E.-1)
((2^(2l+1)[5+6j]) - 1) = 3 Q_j     (C.E.-2)

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9. Those Formulas as Functions and theirs linearity state not only Solved Collatz Conjecture but also brought multiple Science Jewels from results coming from.

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10. Murgu Table2To3 as Collatz Conjecture Unique Solution was validated multiple times by:
Marker USA Murgu Arrow.
Infinity Murgu Table2To3.
Infinity Marker USA Murgu Arrow.
Collatz Conjecture Pocket Map Murgu Table2To3.
Prof of Proof Murgu 1D Array Index Infinity_Per_6.
Index Infinity_Per_6 is a Truth as pure provocation as never can touch Infinity - and an Infinity Paradox.

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11. Collatz Conjecture Murgu Unicity Demonstrated (even was not needed) for Earth Mathematics Community
Murgu Table2To3 is Collatz Conjecture Unique Solution.

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Collatz Conjecture Paradox.

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Collatz Conjecture Into negative Integers loss its sense and it is revealed by
Murgu Conjecture Vicious Redundancy

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which mirror in positives Collatz Conjecture Into Negative.
Collatz Conjecture have all legacy as to represent in negatives Collatz Conjecture in 2-th or 4-th Quadrant. It reflect The Paradox and the truth as
(3x +1) with x negative loss the sense.

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The roots for Collatz Conjecture in Negatives as Collatz Conjecture is are 12 or more
(-1)
(-5) - (-7)
(-17) - (-25) - (-37) - (-55) - (-41) - (-61) - (-91)
Murgu Conjecture Vicious Redundancy revealed those roots but can be more . This is enough to Consider
Collatz Conjecture Into Negative Loss is accurate sense.

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I hope, in time, Earth H-Intel Mathematics Community will accept it!
But Collatz Conjecture into negative can be considered a Paradox as Murgu Conjecture Vicious Redundancy Into Negatives.
(3x - 1) with x negatives values.
Paradox is revealed in quadrant 4 or to 2 as
(-1) (3x + 1) where positive axle (x) is Ox for quadrant 4-th or Oy for Quadrant 2-th.

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Collatz Conjecture can be important for future Logic.

Down can see Murgu Table2To3 Gr. 0 (k=l=0) and Murgu Table2To3 composite part.

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