As will see we in any senses excluded Even Positive Integers From Demonstrating Collatz Conjecture
, but also will observe those are only Passing Nodes , and then are lossing by Property The Carracter
of Collatz Nodes as Collatz Conjecture Falling Nodes. All this don't modify Nothingh as demonstration
and solutions but maybe a single thing
If You Consider those Legal Nodes , Then
Infinity_PER_6 remain or stand-up as every Collatz Conjecture distinc Path will start from Even.
Reminder:
Collatz Conjecture Solutions can't be afforded via PROOFS.
A proof can't certify for Infinity.
Now, via New Murgu Concepts even Binary Proof for Collatz Conjecture
can make a step more , but Infinity don't let it to be more then a Proof.
Then Solution claim accurate DEMONSTRATION and The Problem is
. What to demonstrate for Collatz Conjecture?
Murgu Conjecture Vicious Redundancy show clear one.
DANGER OF LEAF EFFECTS
and then also a possible
ROOT REVERSE TO INFINITY
To demonstrate it need to demonstrate every dual logical Collatz connection possible is a unique
duality for Collatz Procedure and UNITY is Father for all as this dual connection is leading Up To Down.
Collatz Conjecture Explained will be motive of change and add until all with
any Math skill will understood it as Collatz Conjecture wear a lot of Logical Beauty
and 3 important results :
1. Only Human Mind can Image Collatz Conjecture
2. Infinity_Per_6, Collatz Complete Paths (Pats wich have at The Last a different Logical Node)
3. Infinity_Per_18 Logical Trunk Direct Connections(not finished calculation) etc..
This will not affect
Collatz Conjecture Solved
Collatz Conjecture Murgu Arrow as Principal Key Of who brought New Logical Eternal Triads Formulas but
also
Collatz Conjecture Murgu Arrow Dual Linear Noncompeting Functions.
First, Is clear understood for sure
Even Positive Integers Exclusion , as even will return procedural to odd,
because Every Even Positive Integer by one or multiple division with 2 fall in a odd.
This will make a little easy the work in using Murgu Inverse Method via adequate formulas.
Now
To understand Collatz Conjecture even
Collatz Conjecture 3D (or 2D) Apple Tree Corner Web
Logical Representation
Is Important and brought any in, as:
possibility of distinct more
kind of Logical Nodes Connections which also pay respect for Collatz Procedures. This was possible, or revealed
also By Murgu Inverse Method and for it need to deffine function of any logical caracteritics Odd
Integers in 3 category:
1. Logical Dead Nodes or Logical Left Side Closures,
All
Odd Positive Integers which are divided one or more times by 3.
2. LFETN1i ,
Logical First Eternal Triad Node (first as position in Grid)
3. LSETN2i ,
Logical Second Eternal Triad Node (second as position in Grid)
both last 2 and 3 are Logical
Eternal Triads wich share common properties as:
Logical Left Connection(which can be another LETN
or a LDN )
Logical Top Connections which are anothers LETN , are Parts of Infinity as infinity.
Logical Right or Down Connection ofered by (3x+1) itself.
Understanding this logical representation help Collatz Conjecture understanding but also a happy fact
ONLY HUMAN MIND CAN IMAGE - Collatz Conjecture.
Down is a try to see it for a small amount and without check of any error yet, and using
Murgu Inverse Method.
This PNG reveal partially our Inverse Method refering only to odd positive Integers. For Murgu Inverse Method Only Infinity is the barrier in revealing Collatz Conjecture all paths, all connections and all beauty.
All Collatz Conjecture Murgu New Concepts are Logical Connected, but to be explained need to be separed.
Maybe next as importance to be explained is
Perfect Grid To Infinity
For Collatz Conjecture and Murgu Conjecture Vicious Redundancy (mirror image of Collatz Conjecture in
Negative) , ZERO do not exist. Then first tentation is to divide Positive Integer in Grids of 3 components
((1,2,3),(4,5,6), (7,8,9),(10,11,12), ..), but as we saw via Murgu Inverse Method, Even Numbers and Odds
in Grids present small different proprieties. Then it lead us to grids of 6 components as will see those
will share common proprieties for Collatz Procedures .
((1,2,3,4,5,6), (7,8,9,10,11,12),
(13,14,15,16,17,18),..)
As know Murgu Inverse Method and simple observation Even Numbers fall in a odd via Collatz procedures,
let us to work only with Odds, as to easy The Work.
((1,3,5),(7,9,11), (13,15,17),(19,21,23), ..)
As can see every grid contain :
Logical First Eternal Triad Node, LFETN1i
Logical Dead Node or Logical Left Closure LDNi . Logical Left Closure(LDN) is every Odd
divided one or more times by 3. As will see, a LDN do not have Left or Right Connection
but only Down-Right via (3x+1) and this connection will be to a LETN or directly to Trunk , which mean
directly to LETN UNITY.
Logical Second Eternal Triad Node, LSETN2i
Demonstration,
all LDN don't generate Left or Top Connection
Analytic for Perfect Grid To Infinity reveal a lot as :
Every LDN not Left and Top Connection is
verry important because having only Right-Down connection. Then Reverse Logic lead it, automatic is
an LETN . That is more then important, because demonstrate
every LDN have a Unique Connection and is
to a LETN.
Only Collatz Procedures starting from LDN can be Collatz Complete Paths.
A Collatz Procedure Starting from a LDN, in its Path, never will pass(or meet) via another LDN.
A Collatz Procedure Starting from a LETN, in its Path, never will pass(or meet) via a LDN.
This need demonstration and can be right here
A Left Side Connection is revealed By 2 possible Murgu Formulas:
(4di -1 = 3 ui) d is a LDN in grid i
OR
(2di -1 = 3 ui) d is a LDN in grid i
we know d is di = 3 v ehere v an odd
then
(12v -1 = 3 ui)
OR
(6v-1 = 3 ui)
If will note (4v = t ) and (2v = g)
(3t -1 = 3 ui)
OR
(3g-1 = 3 ui)
Impossible
Is Clear this exclude also Top Connections, for any(all) LDN, and Murgu Inverse Method and Reverse Logic
helped a lot.
THIS EXCLUDE LDN FROM DANGERING Collatz Conjecture but via a
MATH OVERPASS THE PROBLEM TO LOGICAL ETERNAL TRIADS
Collatz Conjecture Murgu Arrow will solve it.
A Logical Beauty coming for it
Collatz Conjecture Complete Paths
Infinity_PER_6 .
Murgu Inverse Method and Reverse Logic.
Murgu Inverse Method is based on a first place Reverse Logic of Collatz Conjecture Procedure (3x+1).
As we excluded virtual Even Numbers, then we can redirect this procedure to Odds via
((3x+1)=(2k)o) where x and o Odds k Positive Integer
((((2k)o)-1)=3x) base formula for Murgu Inverse Method
As will see Murgu Inverse
Method is leaded by 4 Formulas and a applied only to Logical Eternal Triad including Unity .
Now can make Javascript , Perl, C++, C, C#, Rust , etc., which to reveal Collatz Conjecture Paths, but
limit remain Infinity also for every programing language.
Infinity_PER_6
then, prov
ONLY HUMAN MIND CAN IMAGE COLLATZ CONJECTURE and USA_AEPDF
Now a simple observation, we have in every grid 2 kind of Logical Eternal Triads,
Logical First Eternal Triad Node, LFETN1i
and
Logical Second Eternal Triad Node, LSETN2i
with simple Math motivated conditions will separe it in 2. To note LFETN1i with
W1i and LSETN2i with W2i , those will be :
((((22k)o)-1)=3W1i) k >0
((((22k+1)o)-1)=3W2i) k >=0
Via those Equations an using added skill about Perfect Grids To Infinity, now can make
programs in Javascript, Perl, C++ which to generate all Collatz Conjecture Paths, but
Infinity is a big issue even for Computers
Sory to repeat, but to remind to everyone, we can be proud,
Anyway PROV
ONLY HUMAN MIND CAN IMAGE COLLATZ
CONJECTURE
From those 2, we extract also 2 to make distinct Left Side Connection node from Top's.
((4o)-1=3W1i)
((((2)o)-1)=3W2i)
THOSE 2 EQUATION HAVE BIG IMPORTANCE FOR
Collatz Conjecture Solutions
As saw before excluded LDN as "PROBLEM" from, BY Passing it To Logical Eternal Triads
and as will see are base for solving it there via Collatz Conjecture Murgu Arrow.
Here is a Link for:
Maybe also Logical Eternal Triads need a small Explanation,
First, I insisted for The Name "Logical Eternal Triad" as express perfect those entities.
Those refer 3 Connections, Left, Top and Right-Down - then Triad. Top Connections are infinity,
generating eternal connections to Infinity.
As already know a grid contain 3 Odds Numbers. One is a Logical Dead Node and guarded in the front
and back by 2 Logical Eternal Triads which virtual , using Murgu Inverse Method every one "generate"
infinity(Part of Infinity ) Logical Nodes any times are LDN .
As know LDN leave all the weight on Eternal Triad - and it - lead to
Table 2 To 3
which to reveal if possibly all Logical Eternal Triads Left Side Connections.
Possisibly mean - leaded via Functional - then to determine, in our case, 2 function which to
certify Unicity for this Dualism.
this mean, if exist, all Essence Connections (Left Connections ) assure for Collatz Procedure
(Reverse Logic aspect- left with right) unicity for way Down to UNITY.
And will see
Collatz Conjecture Murgu Arrow
did it. There we initialy did , fastening,
a small confusion or indices , but for a Math skilled is nothing.
As we will expose next Collatz Conjecture Murgu Formulas, down is a link if wish to pass
Collatz Conjecture Solutions.
was brought by
Collatz Conjecture Murgu Arrow
short
Murgu Arrow
which wear it in new dress.
Collatz Conjecture New Name -Infinity_Per_6
A Poetic Truth.
Collatz Conjecture Murgu Arrow
new 8 Collatz Murgu Formulas
Perfect Grid To Infinity
Eternal Triad and LLDN
brought for, or wear
Collatz Conjecture
in Beauty Logical and
first EXACT INFINITY REFERENCE
Infinity_PER_6
Every Murgu New Collatz Conjecture Concepts have importance on, even ,
3D Collatz Conjecture
Logical Apple Tree Representation
and it because only Human can Mind Image it, and is important.
Also , Murgu Collatz Conjecture String Locators Formulas, for locating : grids, 2 for
Logical Eternal Triads and one for Logical Dead Nodes.
Keep in mind , Murgu Arrow show only Eternal Triads Left Connection Node , when for a
Mind Image need to not forgot Top which are infinity for every Eternal Triad
,
where infinity is a part of Infinity and can't be defined exactly. Instead
Infinity_PER_6
can
Complete Paths Number
and also Number of Perfect Grids. Then
Collatz Conjecture Murgu Arrow is principal key of
Collatz Conjecture Solved,
BUT Also Collatz Conjecture Murgu Formulas play an essence roll in.
As key of Collatz Conjecture Solved, I will keep Collatz Conjecture Murgu Arrow Link.
MURGU FORMULAS (IN LOGICAL MIRROR)ASSURE LOGICAL CONTINUITY AND UNICITY for A DUAL LOGICAL CONNECTION FOR ALL ODDS TO INFINITY FOR
COLLATZ PROCEDURES
THEN FOR ALL POSITIVE INTEGER.
MURGU FORMULAS can be 12 , but important are 8. That because can exclude Murgu Lemas(2)
, and unity 4 for LET in 2. To understand theirs role, need to see
any new concepts in, as:
6 components Grids to Infinity
Collatz Procedures used via logical reverse Murgu Inverse Method
Observation, logical can exclude Positive Even Integers to easy content
then , a Grid will contain 2 Logical Eternal Triad and a Logical Dead Nodes
MURGU FORMULAS
4 Collatz Conjecture Murgu String Locators Formulas
Grid Locator Gi = 1 + 6i
First Logical Eternal Triad Locator (LET1)i = 1+6i
Second Logical Eternal Triad Locator (LET1)i = 5+6i
Logical Dead Node Locator (LDN)i = 0+3i i>0 and i odd only
Now, will folow 6 new Formulas which are essence of solution for Collatz Conjecture.
2 of them are used for a long time , but without positive results.
2 of them are like 4, obtained in exercise to rebuild Collatz Conjecture starting from Unity,
Collatz Conjecture Murgu Inverse Method.
Those refer only Logical Eternal Triad , but Logical Keft Dead Nodes are not uncovered. Those
don't have Left And Top Logical Connections , then only one which is Logical Right And Down. Then for
moment can be out of our imediat scope and return separately to it.
Those are:
(2(2k) v1i -1 = 3 ui) for LET1
(2(2k+1)v2i -1 = 3 ui) for LET2
where v1i is a ET , first in Grid and v2i is a ET , second in Grid i
Those are Logical Top Commections, are infinity but as will see every one assure duality and unicity for Collatz
Procedure. Logical Top Commections do not affect Murgu Arrow , because every one is coming as Right-Down from
anoter LETN wich is (3x+1) formula.
Discovering of infinity as Infinity Parts fact prove
ONLY HUMAN CAN IMAGE COLLATZ CONJECTURE
Image here play a role of verb , action.
Murgu Inverse Method Separed from Those Formulas 2 as Left Side
Logical Connections:
(4v1i -1 = 3 ui) for LLETN1
(2v2i -1 = 3 ui) for LLETN2
where v1i is a ET , first in Grid and v2i is a ET , second in Grid i
Those last 2 have importance in demonstrating unicity of logical connections and even in geting Collatz Conjecture
Murgu Arrow Formulas.
Collatz Conjecture Murgu Arrow , became essence key for Collatz Conjecture Solutiomn.
Maybe Logical forte point of Collatz Conjecture Murgu Arrow is
TABLE 2 TO 3
WHICH is possible because in Collatz Conjecture Perfect Grids To Infinity in everi Grid , for logical analytic,
remain 3 Components LETN1i, LDNi and LETN2i (where i is grid indice and 1 or 2
ET position in grid) .
Because LDN don't have Left Connection we can make this table which reveal 2 New
Collatz Conjecture Murgu Formulas which can offer closure for .
Errata
In first published Murgu
Arrow material, I Don't make special important specification :
Murgu Arrow formulas are offering every Left
Logical Side ET Node Connection which can to be any times a LDN(it was seid) , and in reality for every kind of
ET at every third time. Then Formulas will be:
LFETNC1(i+1) = LFETNC1(i) + 8 for i grid indice,1 position
LSETNC2(i+1) = LSETNC2(i) + 4 for i grid indice,2 position
This do not affect demonstration , are only conventional remark with role of distinction.
Those Formulas offer to
Collatz Conjecture to be exactly to Collatz Procedures, Liniarity, Unicity and important , not
Concurency , as between W1i and W2i stand up 5 as not 2 divisible.
As known, Logical Left Side Dead Nodes or Logical Left Side Closures do not present a Possible Danger on
Logical Leaf Effect (Logical Circle Rotation via Collatz Procedures)
or, Root Reversion to Infinity.
Anyway , If we Want to make more study for and on
Left Side Dead Nodes or Logical Left Side Closures
Murgu 3XPlus3 Conjecture and (3X-3) may be a help.
Now, via new concepts exposed For Mathematics , Collatz Conjecture present 2 dangers:
Leaf Effect as Murgu Conjecture Vicious Redundancy which create multiple roots.
reverse root to Infinity which mean to exist any positive Integer for which via Collatz Procedures never to fall in Unity.
To eliminate all Doubts I will keep also old Collatz Conjecture Murgu Arrow Demonstration
which in essence is correct
For, Collatz Conjecture Murgu Arrow Beauty Logical
Collatz Conjecture Murgu Arrow
If You remind , we got, in a 3D APLLE Tree Logical Representation Analyse, Positive Integers Separated
-in 6 Components Perfect Grids To Infinity.
Every One(grid) Contain a Logical Left Side Dead Node, and 2 Logical Eternal Triad Generators Which Differ
by Murgu Collatz Conjecture Formulas(4kW or 2kW)
First (LETGN1): (4W-1)/3 - Second(LETGN2) in Grid: (2W-1)/3
generate Left Side
new connection, LETGN or LLDN and also To TOP Will Be generayed infinity(FOR LETG only).
For This Scope we Generated A Table where First Column folow Grids Eternal Triads Only abd Top Row
Grids Eternal Triads and Dead Nodes(results of Murgu Formulas for Left connections).
The Table is Down Table 2To3
The Table we get can be considered Consistent Proof, but we Demonstrated which those undreds proofs show.
But Table reveal a Small Math Beauty
Collatz Conjecture Murgu Arrow
and
If whish to extend The Table became easy task.
As see a edge of arrow evolve by +4 to last, and another edge by +8 to the last
AND Every Edge is provided by first ET in the grid and second edge by sec. in the grid.
The table Show for Every Eternal Triad we have a Left Side Connection
and Its Lefta Side Connction via Collatz Procedure Fall In It.
Apparent we are losing any Dead Nodes or Left side Closures
This is hapening because Table is 2To3 and important is Logical Eternal Triads can't be.
Those are going direct into Logical Trunk then Unity. Example 21 - (21x3 +1)=64.
Table 2To3 became Principal Key Of Collatz Conjecture Solution, because if can be demonstrate
those dual dependencies , then clear wil guarde Collatz Conjecture with 2 linear functionality.
Like said before, LDN passing all weight on Logical Eternal Triads lead us to a
Table 2To3 ANALYTIC
Eternal Triads - Table 2To3
and did it using Murgu Inverse Method 2 Murgu Formulas for geting Logical
Left nodes connection. As we have 2 kind of Eternal Triads , will note those as
LLFNC1i, where 1 - first in grid i, LLSNC2i where 2 - second in grid i .
To substitute those for easy with
T1i, where 1 - first in grid i, T2i where 2 - second in grid i .
Building the tabel for, can't to escape from observation a fact revealed down
T1(i+1) = T1i + 8
T2(i+1) = T2i + 4
But, even if we have a lot of proofs for , we can legalize those linear functions but only after
demonstration. We can do it via 2 Methods.
By geting T1(i+1) and T2(i+1) , then T1(i) and T2(i)
from anything else and compare.(Method 1)
Or, using Add Absurd.(Method 2)
For it need to connect
T1(i+1) and T2(i+1), T1(i) and T2(i)
to theirs Logical Eternal Triads via Murgu formulas.
(3(T1(i+1))) = (4(W1(i+1))-1) E.1
(3(T1(i))) = (4(W1(i))-1) E.2
we know also (W1(i+1)) = ((W1(i))+6) and then E.1 can be write
(3(T1(i+1))) = (4(W1(i))-1+24) E.1
or (3(T1(i+1))) = ((3(T1(i)))+24) and dividing by 3
T1(i+1) = T1i + 8
for Logical Eternal Triad Second position in grid
(3(T2(i+1))) = (2(W2(i+1))-1) F.1
(3(T2(i))) = (2(W2(i))-1) F.2
we know also (W2(i+1)) = ((W2(i))+6) and then F.1 can be write
(3(T2(i+1))) = (4(W2(i))-1+12) F.1
or (3(T2(i+1))) = ((3(T2(i)))+12) and dividing by 3
T2(i+1) = T2i + 4
For Method 2 can consider old one EXPOSED IN OLD MATERIALS
THIS DEMONSTRATION CERTIFY 2 NEW FUNCTIONS FOR COLLATZ CONJECTURE.
THOSE SHOW LINEARITY, AND THEN, NOT CONCURENCY FOR -
EXCLUDE LEAF EFFECT AND MAKE THE SENSE INFINITY TO UNITY (BY REVERSE LOGIC) UNIQUE.
Those can be connected to grid position into defined Perfect Grid to Infinity , where first grid
is 0.
For First Logical Eternal Triad in Grid i, its Logical Left Connection wiil be
LLETC1i = 1 + 8i where i is Grid i LETN position 1. FC.1
For Second Logical Eternal Triad in Grid i, its Logical Left Connection wiil be
LLETC2i = 3 + 4i where i is Grid i LETB position 2. FC. 2
To hope not anoter notations mistakev ! Anyway FC.1 and FC.2 can be verified as True.
— Collatz Conjecture
SOLVED —
2 Solutions for Collatz Conjecture
WE DEMONSTRATED(and brought) 2 IMPORTANT FUNCTIONS FOR Collatz Conjecture via
Collatz Conjecture Murgu Arrow
that closed Collatz Conjecture whith A Beauty Logical SOLUTION
Apparent any is loss there , but is nothing more then a confusion made by Reverse Logical
understanding .
For it we make an another table for the same Logical Eternal
Triads (the same Grids) but Logical Right-Down Connections, as to see how Collatz Procedure create
apparent Logical Divergence
First 6 grids Logical Eternal Triads Collatz Procedure Connections.
Any LDN do not appear into table 2To3 because are Top Connections of UNITY as generators
and fall direct into Trunk.
Example 21 is a LDN and determine a Collatz Path with 21 - Unity via (3x+1)
(3(21) + 1) = (63 + 1) =64
Also 85 , BUT AS LETGN
Those can be refered to Infinity like Infinity_PER_6 and if not mistake are
Infinity_PER_18 as fasting calculus.
now can say
Collatz Conjecture SOLVED
Collatz Conjecture HAVE SOLUTION
Murgu Inverse Method Excluded EVEN Positive Integers from
I will say vi a right motivation
As Logical Falling Nodes. AND to introduce them as Collatz Nodes change only Collatz Conjecture
Complete Paths , for
Infinity_PER_6 To Infinity_PER_3 .
Table 2TO3 Show Unicity for every Eternal Triad Collatz Procedure related.
For 1/3 (Odds Numbers part)Logical Dead Nodes Uncovered BUT
That is because are Direct Logical
Dead Nodes to Unity via Trunk.
REMINDER: Every Logical Dead Nodes have unique connection right-down to a LETN including Unity
,
then is covered also here as those are n's connection of a Dead Nodes to a LETN. For our final demonstration
Infinity Pay Respect for Collatz Procedure
This is not a problem
Above I gave an example 21, and another can be 45 Wich is second connection of 17 as first top one.
Left Side connection for 17 is 11, when Top first one is 45.
Collatz Conjecture Murgu Arrow , became essence key for Collatz Conjecture Solutiomn.
Maybe Logical forte point of Collatz Conjecture Murgu Arrow is
TABLE 2 TO 3
WHICH is possible because in Collatz Conjecture Perfect Grids To Infinity in everi Grid , for logical analytic,
remain 3 Components LETN1i, LDNi and LETN2i (where i is grid indice and 1 or 2
ET position in grid) .
Because LDN son't have Left Connection we can make this table which reveal 2 New
Collatz Conjecture Murgu Formulas which can offer closure for .
Collatz Conjecture Murgu Arrow Logical Eternal Triads Formulas as
Murgu Dual Linear Noncompeting Functions
Demonstrated
Every Logical Eternal Triad LeftSide Connection is Unique Bigest Then Logical Eternal Value,
AND not Concurency as Not 2 of them can have the same.
LLETC1i = 1 + 8i where i is Grid i LETN position 1. FC.1
LLETC2i = 3 + 4i where i is Grid i LETB position 2. FC. 2
Eliminate possibility Of Leaf Effects and Reorder Collatz Conjecture Apparent Divergence to Unique
Evolving Direction Infinity To UNITY . NOT Reverse ROOT
Collatz Conjecture Solved
Infinity Pay Respect for Collatz Procedure
To understand Math Logical Play Divergence
to Functional Convergence Compare
First 6 grids Logical Eternal Triads Collatz Procedure Connections.
WITH
Table 2To3
Nothing Math Logical can't contest here, reverse logical Left Connections Formulas because are
coming from "mirroring" Collatz Procedure itself excluding maybe small nottations errors .
Down is Table 2To3, also old Collatz Conjecture Murgu Arrow . but also which may present interest.
Any Example which can help understanding at link:
For, helping example
1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | 57 | 59 | 61 | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 79 | 81 | 83 | 85 | 87 | 89 | 91 | 93 | 95 | 97 | 99 | 101 | 103 | 105 | 107 | 109 | 111 | 113 | 115 | 117 | 119 | 121 | 123 | 125 | 127 | 129 | 131 | 133 | 135 | 137 | 139 | 141 | 143 | 145 | 147 | 149 | 151 | 153 | 155 | 157 | 159 | 161 | 163 | 165 | 167 | 169 | 171 | 173 | 175 | 177 | 179 | 181 | 183 | 185 | 187 | 189 | 191 | 193 | 195 | 197 | 199 | 201 | |||||||||||||||||||||||
1 | 1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
5 | 3 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
7 | 9 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
11 | 7 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
13 | 17 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
17 | 11 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
19 | 25 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
23 | 15 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
25 | 33 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
29 | 19 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
31 | 41 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
35 | 23 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
37 | 49 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
41 | 27 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
43 | 57 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
47 | 31 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
49 | 65 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
53 | 35 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
55 | 73 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
59 | 39 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
61 | 81 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
65 | 43 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
67 | 89 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
71 | 47 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
73 | 97 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
77 | 51 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
79 | 105 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
83 | 55 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
85 | 113 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
89 | 59 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
91 | 121 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
95 | 63 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
97 | 129 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
101 | 67 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
103 | 137 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
107 | 71 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
109 | 145 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
113 | 75 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
115 | 153 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
119 | 79 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
121 | 161 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
125 | 83 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
127 | 169 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
131 | 87 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
133 | 177 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
137 | 91 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
139 | 185 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
143 | 95 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
145 | 193 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
149 | 99 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
151 | 201 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
155 | 103 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
This Table 2To3 is possible because: 1. Logical Dead Nodes don't have Logical Left and Top Connections. 2. are Murgu Inverse Method to reveal Logical Left Eternal Triads Connection.
1 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 | 35 | 37 | 41 | 43 | 47 | 49 | 53 | 55 | 59 | 61 | 65 | 67 | 71 | 73 | 77 | 79 | 83 | 85 | 89 | 91 | 95 | 97 | 101 | 103 | 107 | 109 | 113 | 115 | 119 | 121 | 125 | 127 | 131 | 133 | 137 | 139 | 143 | 145 | 149 | 151 | 155 | 157 | 161 | 163 | 167 | 169 | 173 | 175 | 179 | 181 | 185 | 187 | 191 | 193 | 197 | 199 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
1 | 1 | 11 | 17 | 5 | 13 | 29 | 35 | 19 | 11 | 47 | 53 | 7 | 31 | 65 | 71 | 37 | 5 | 83 | 89 | 23 | 49 | 101 | 107 | 55 | 29 | 119 | 125 | 1 | 67 | 137 | 143 | 73 | 19 | 155 | 161 | 41 | 85 | 173 | 179 | 91 | 47 | 191 | 197 | 25 | 103 | 209 | 215 | 109 | 7 | 227 | 233 | 59 | 121 | 245 | 251 | 127 | 65 | 263 | 269 | 17 | 139 | 281 | 287 | 145 | 37 | 299 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
Table 2To2 which show for first 34 Grids Logical Eternal Triads Collatz Procedure Connections.
Instead Of Table 2To3 Reverse Logic, here became clear divergence on.
In Collatz Conjecture
Infinity darts Unity Via
Collatz Conjecture Murgu Arrow.
Collatz Conjecture Murgu Arrow used Murgu Collatz Conjecture Inverse Method but only
to reveal for every Logical Eternal Triad Generarators only Logical Left Side Connection.
COLLATZ CONJECTURE SOLVED
WE DEMONSTRATED LOGICAL DEAD NODES ARE LEFT SIDE CLOSURES
THOSE CAN'T EVOLVE LEFT SIDE CONNECTIONS.
A COLLATZ PROCEDURE STARTING FROM LOGICAL ETERNAL TRIAD , NEVER WILL MEET OR PASS
ANY LDN , LLDN.
COLLATZ PROCEDURES STARTING FROM LLDN ALSO WILL NOT PASS OR MEET ANOTHER LLDN, AND VIRTUAL
AS TO DEFINE ALL COLLATZ PATHS CA BE RELATED AS COMPLETE PATH FOR ITS DEAD NODE
ALL COLLATZ COMPLETE PATHS ARE INFINITY/6 (∞/6)
NOW
Collatz Conjecture Murgu Arrow (VIA New Formulas) Cover Totaly Collatz Conjecture and
brought(implay also Murgu Inverse Method) for it Logical Continuity which
Math can to afford now for Collatz Conjecture.
Even Collatz Paths are covered there , with a mention
for Logical Left Dead Nodes or Logical Left Closures node Logical Right Eternal Triad Connection can be obtained using one time Collatz Procedure.
Now Perfect Grid To Infinity
became easy for using
REDUCTION AD ABSURD
6 Components Positive Integers began to number with 0 , because of 0 grid assymmetry.
Now, to remind any important things before start:
don't forgot Murgu Lemas, Murgu Collatz Conjecture Formulas
in a grid have 2 kind of Eternal Triad
Collatz Conjecture Murgu Arrow Formulas
Now to consider by absurd for grid K for both Eternal Triads is a Truth that will have
a Left Connection another Eternal Triads or Dead Nodes .
Then If for Grid (K + 1) also this is a truth
For Collatz Conjecture is a truth
do not present Root Reversion or Leaf Effect.
I repeat for Dead nodes do not need to do it as those have only rigths side connections wich are
to a eternal triad or direct onto Trunk to Unity.
To take a grid Nr. K and to analyze it for Grid (K + 1)
As known, First Eternal Triad grid K will be (6K + 1)
and in (K + 1), (6K + 7)
Then: Via Murgu Formulas
COLLATZ CONJECTURE SOLVED
Keys for:
Perfect Grid To Infinity
Murgu String Locators Formulas
Reverse Logic
Murgu Inverse Method
Collatz Conjecture Murgu Arrow.
Logical Dead Nodes demonstrated Exclusion from Problem Creators.
Logical Eternal Triads 2To3 Table.
New Reverse Logic Collatz Conjecture Murgu Dual Linear Functions .
DEMONSTRATED via Math rules.
Logical Eternal Triads First Left Connection Murgu Formulas
Logical Eternal Triads Top Connection Murgu Formulas
Maybe even Murgu Lemas hided in LDN not Logical Left and Top Connections>
and 3D(2D) Logical APPLE Tree Corner Web Collatz Conjecture Representation .
and we get First Infinity Exact Reference
Infinity_PER_6.
Make 86 unsolved Problem
COLLATZ CONJECTURE SOLVED
as Brilliant
Earth Science AND Culture Event.
Human Intelligence Victory.
Down, is a try image of a inverse method starting from Unity incomplete and maybe any small errors , but can help for Understanding.
This PNG reveal partially our Inverse Method refering only to odd positive Integers. Only Infinity is the barrier in revealing Collatz Conjecture all paths, all connections and all beauty.
Eternal Triads Top Connections , infinity, appear via a Murgu Formulas, because Infinity connections
can't imaged. Those can be Imaged only in Human mind . Need to remark, for Collatz Procedures , every one
present Unicity.
Collatz Conjecture Solution
Collatz Conjecture Murgu Arrow
Down I will keep yet any tables wich can be used in understanding and everyone can contribute in times.
999 | 1499 | 2249 | 1687 | 2531 | 3797 | 89 | 67 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 16 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
3997 | 1499 | 2249 | 1687 | 2531 | 3797 | 89 | 67 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 16 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
This Table Show how Collatz Conjecture Murgu Inverse Method can Complete a Collatz Path.
- | - | Grid | Nr | 31 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
187 | 281 | 211 | 317 | 119 | 179 | 269 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 1 | ||||||||||||||||||||||||||||||||||||||||||||||||
187 | 249 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
191 | 287 | 215 | 323 | 485 | 91 | 137 | 103 | 155 | 233 | 175 | 263 | 395 | 593 | 445 | 167 | 251 | 377 | 283 | 425 | 319 | 479 | 719 | 1079 | 1619 | 2429 | 911 | 1367 | 2051 | 3077 | 577 | 433 | 325 | 61 | 23 | 35 | 53 | 5 | 1 | ||||||||||||||||||||||||
191 | 127 | 169 | 225 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- | - | Grid | Nr | 32 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
193 | 145 | 109 | 41 | 31 | 47 | 71 | 107 | 161 | 121 | 91 | 137 | 103 | 155 | 233 | 175 | 263 | 395 | 593 | 445 | 167 | 251 | 377 | 283 | 319 | 479 | 719 | 1079 | 1619 | 2429 | 911 | 1367 | 2051 | 3077 | 577 | 433 | 325 | 61 | 23 | 35 | 53 | 5 | 1 | ||||||||||||||||||||
193 | 171 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
197 | 37 | 7 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
197 | 131 | 87 | LLDN | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- | - | Grid | Nr | 33 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
199 | 299 | 449 | 337 | 253 | 95 | 143 | 215 | 323 | 485 | 91 | 137 | 103 | 155 | 233 | 175 | 263 | 395 | 593 | 445 | 167 | 251 | 377 | 283 | 425 | 319 | 479 | 719 | 1079 | 1619 | 2429 | 911 | 1367 | 2051 | 3077 | 577 | 433 | 325 | 61 | 23 | 35 | 53 | 5 | 1 | |||||||||||||||||||
199 | 353 | 235 | 313 | 417 | LLDN | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
203 | 305 | 229 | 43 | 65 | 49 | 37 | 7 | 11 | 17 | 13 | 5 | 1 | ||||||||||||||||||||||||||||||||||||||||||||||||||
203 | 135 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- | - | Grid | Nr | 40 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
241 | 181 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
241 | 321 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
245 | 23 | 35 | 53 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
245 | 163 | 217 | 289 | 385 | 513 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- | - | Grid | Nr | 45 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
271 | 407 | 611 | 917 | 43 | 65 | 49 | 37 | 7 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||
271 | 361 | 481 | 641 | 427 | 569 | 379 | 505 | 673 | 897 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||
275 | 413 | 155 | 233 | 175 | 263 | 395 | 593 | 445 | 167 | 251 | 377 | 283 | 425 | 319 | 479 | 719 | 1079 | 1619 | 2429 | 911 | 1367 | 2051 | 3077 | 577 | 433 | 325 | 61 | 23 | 35 | 53 | 5 | 1 | ||||||||||||||||||||||||||||||
275 | 183 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- | - | Grid | Nr | 73 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
439 | 659 | 989 | 371 | 557 | 209 | 157 | 59 | 89 | 67 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||
439 | 585 | LLDN | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
443 | 665 | 499 | 749 | 281 | 211 | 317 | 119 | 179 | 269 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||
443 | 295 | 393 | LLDN | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Example of Generating Collatz Conjecture Complete Paths Starting from an Eternal Triad and using both Procedures.
999 | 1499 | 2249 | 1687 | 2531 | 3797 | 89 | 67 | 101 | 19 | 29 | 11 | 17 | 13 | 5 | 1 | ||||||||||||||||||||||||||||||||||||||||||||
993 | 745 | 559 | 839 | 1259 | 1889 | 1417 | 1063 | 1595 | 2393 | 1795 | 2693 | 505 | 379 | 569 | 427 | 641 | 481 | 361 | 271 | 407 | 611 | 917 | 43 | 65 | 49 | 37 | 7 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||
987 | 1481 | 1111 | 1667 | 2501 | 469 | 11 | 17 | 13 | 5 | 1 | |||||||||||||||||||||||||||||||||||||||||||||||||
981 | 23 | 35 | 53 | 5 | 1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||
975 | 1463 | 2195 | 3293 | 1235 | 1853 | 695 | 1043 | 1565 | 587 | 881 | 661 | 31 | 47 | 71 | 107 | 161 | 121 | 91 | 137 | 103 | 155 | 233 | 175 | 263 | 395 | 593 | 445 | 167 | 251 | 377 | 283 | 425 | 319 | 479 | 719 | 1079 | 1619 | 2429 | 911 | 1367 | 2051 | 3077 | 577 | 433 | 325 | 61 | 23 | 35 | 53 | 5 | 1 | ||||||||
969 | 727 | 1091 | 1637 | 307 | 461 | 173 | 65 | 49 | 37 | 7 | 11 | 17 | 13 | 5 | 1 | ||||||||||||||||||||||||||||||||||||||||||||
Example: Logical Dead Nodes are Complete Collatz Conjecture Paths.
For ,any small grammar , I hope, errors, I will return when time for.
1. All Collatz Conjecture Murgu New Concepts are needed.
for geting
Collatz Conjecture Solutions
and
Collatz Conjecture Solved