Given A=∈1⅄(φ/Q)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so 

A=∈1⅄(φn2/1⅄Qn1)cn 

and 

A=∈1⅄(φn2/2⅄Qn1)cn

then

An1 of 1⅄(φn2/1⅄Qn1)=(1/1.5)=0.^6

An2 of 1⅄(φn3/1⅄Qn2)=(2/1.^6)=1.25 and An2 of 1⅄(φn3/1⅄Qn2c2)=(2/1.^66)=^1.2048192771084337349397590361445783132530

An3 of 1⅄(φn4/1⅄Qn3)=(1.5/1.4)=1.0^714285

An4 of 1⅄(φn5/1⅄Qn4)=(1.^6/1.^571428) and An4 of 1⅄(φn5c2/1⅄Qn4)=(1.^66/1.^571428) and An4 of 1⅄(φn5/1⅄Qn4)=(1.^6/1.^571428571428) and An4 of 1⅄(φn5/1⅄Qn4)=(1.^66/1.^571428571428) and so on for cn variant of An4 of 1⅄(φn5/1⅄Qn4)

An5 of 1⅄(φn6/1⅄Qn5)=(1.6/1.^18)=^0.988875154511742892459826946847960444993819530284301606922126081582200247218788627935723114956736711990111248454882571075401730531520395550061804697156983930778739184177997527812113720642768850432632880

An6 of 1⅄(φn7/1⅄Qn6)=(1.625/1.^307692)

An7 of 1⅄(φn8/1⅄Qn7)=(1.^615384/1.^1176470588235294)

An8 of 1⅄(φn9/1⅄Qn8)=(1.^619047/1.^210526315789473684)

An9 of 1⅄(φn10/1⅄Qn9)=(1.6^1762941/1.^268695652173913043478)

An10 of 1⅄(φn11/1⅄Qn10)=(1.6^18/1.^0689655172413793103448275862)

An11 of 1⅄(φn12/1⅄Qn11)=(1.^61797752808988764044943820224719101123595505/1.^193548387096774)

An12 of 1⅄(φn13/1⅄Qn12)=(1.6180^5/1.^108)

An13 of 1⅄(φn14/1⅄Qn13)=(1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/1.^04878)

An14 of 1⅄(φn15/1⅄Qn14)=(1.6183^0223896551724135014/1.^093023255813953488372)

An15 of 1⅄(φn16/1⅄Qn15)=(1.618^032786885245901639344262295081967213114754098360655737704918/1.^12765957446808510638297872340425531914893610702)

An16 of 1⅄(φn17/1⅄Qn16)=(1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843/1.^1132075471698)

An17 of 1⅄(φn18/1⅄Qn17)=(1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.^0338983050847457627118644067796610169491525423728813559322)

An18 of 1⅄(φn19/1⅄Qn18)=(1.6180340557314241486068^11145510835913312693/1.^098360655737704918032786885245901639344262295081967213114754)

An19 of 1⅄(φn20/1⅄Qn19)=(1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.^059701492537313432835820895522388)

An20 of 1⅄(φn21/1⅄Qn20)=(1.6^1803399852/1.^02816901408450704225352112676056338)

An21 of 1⅄(φn22/1⅄Qn21)=(1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.^08219178)

An22 of 1⅄(φn23/1⅄Qn22)=(1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^96792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/1.^0506329113924) and so on for variables of cn to set variables beyond An22 of 1⅄(φn23/1⅄Qn22) of ∈An of ⅄(φn2/1⅄Qn1)cn 

so if A=∈1⅄(φn2/1⅄Qn1)cn 

and 

A=∈1⅄(φn2/2⅄Qn1)cn

then

An1 of 1⅄(φn2/2⅄Qn1)=(1/0.^6)

An2 of 1⅄(φn3/2⅄Qn2)=(2/0.6)

An3 of 1⅄(φn4/2⅄Qn3)=(1.5/0.^714285)

An4 of 1⅄(φn5/2⅄Qn4)=(1.^6/0.^63)

An5 of 1⅄(φn6/2⅄Qn5)=(1.6/0.^846153)

An6 of 1⅄(φn7/2⅄Qn6)=(1.625/0.^7647058823529411)

An7 of 1⅄(φn8/2⅄Qn7)=(1.^615384/0.^894736842105263157)

An8 of 1⅄(φn9/2⅄Qn8)=(1.^619047/0.^8260869565217391304347)

An ultimate and eventual equation of A variable set then includes a function such as An1 of 1⅄(2φn2/2Qn1) or 

An1 of 1⅄(3φn2/3Qn1) such that Q is a variable of further division tier paths of Q divided by Q ratios just as phi  ratios are potential to definitions and variables. Then on to further complex functions of A of (φ/J), A of (φ/K), A of (φ/L), and A of (φ/U) are definable to variable set ∈A

Functions then X, +⅄, and -⅄ of set A variables φn/1⅄Qn and φn/2⅄Qn replaced where functions of division paths 1⅄,  2⅄, and 3⅄ formulate  A of X(φnx1⅄Qn),  A of X(φnx2⅄Qn),   A of +⅄(φnx+1⅄Qn),  A of +⅄(φn+2⅄Qn),   A of -⅄(φn-1⅄Qn), and A of -⅄(φn-2⅄Qn) so then

if A of X(φnx1⅄Qn) and  A of X(φnx2⅄Qn) then

An1 of X(φn2x1⅄Qn1)=(1x1.5)

An2 of X(φn3x1⅄Qn2)=(2x1.^6)

An3 of X(φn4x1⅄Qn3)=(1.5x1.4)

An4 of X(φn5x1⅄Qn4)=(1.^6x1.^571428)

An5 of X(φn6x1⅄Qn5)=(1.6x1.^18)

An6 of X(φn7x1⅄Qn6)=(1.625x1.^307692)

An7 of X(φn8x1⅄Qn7)=(1.^615384x1.^1176470588235294)

An8 of X(φn9x1⅄Qn8)=(1.^619047x1.^210526315789473684)

so if A of X(φn2x1⅄Qn1)cn 

and 

A of X(φn2x2⅄Qn1)cn

then

An1 of X(φn2x2⅄Qn1)=(1x0.^6)

An2 of X(φn3x2⅄Qn2)=(2x0.6)

An3 of X(φn4x2⅄Qn3)=(1.5x0.^714285)

An4 of X(φn5x2⅄Qn4)=(1.^6x0.^63)

An5 of X(φn6x2⅄Qn5)=(1.6x0.^846153)

An6 of X(φn7x2⅄Qn6)=(1.625x0.^7647058823529411)

An7 of X(φn8x2⅄Qn7)=(1.^615384x0.^894736842105263157)

An8 of X(φn9x2⅄Qn8)=(1.^619047x0.^8260869565217391304347)

AND IF A of +⅄(φnx+1⅄Qn) then A of +⅄(φn+2⅄Qn)then 

An1 of +⅄(φn2+1⅄Qn1)=(1+1.5)

An2 of +⅄(φn3+1⅄Qn2)=(2+1.^6)

An3 of +⅄(φn4+1⅄Qn3)=(1.5+1.4)

An4 of +⅄(φn5+1⅄Qn4)=(1.^6+1.^571428)

An5 of +⅄(φn6+1⅄Qn5)=(1.6+1.^18)

An6 of +⅄(φn7+1⅄Qn6)=(1.625+1.^307692)

An7 of +⅄(φn8+1⅄Qn7)=(1.^615384+1.^1176470588235294)

An8 of +⅄(φn9+1⅄Qn8)=(1.^619047+1.^210526315789473684)

so if A of +⅄(φn2+1⅄Qn1)cn 

and 

A of +⅄(φn2+2⅄Qn1)cn

then

An1 of +⅄(φn2+2⅄Qn1)=(1+0.^6)

An2 of +⅄(φn3+2⅄Qn2)=(2+0.6)

An3 of +⅄(φn4+2⅄Qn3)=(1.5+0.^714285)

An4 of +⅄(φn5+2⅄Qn4)=(1.^6+0.^63)

An5 of +⅄(φn6+2⅄Qn5)=(1.6+0.^846153)

An6 of +⅄(φn7+2⅄Qn6)=(1.625+0.^7647058823529411)

An7 of +⅄(φn8+2⅄Qn7)=(1.^615384+0.^894736842105263157)

An8 of +⅄(φn9+2⅄Qn8)=(1.^619047+0.^8260869565217391304347)

AND IF A of -⅄(φnx-1⅄Qn) then A of -⅄(φn-2⅄Qn)then 

An1 of -⅄(φn2-1⅄Qn1)=(1-1.5)

An2 of -⅄(φn3-1⅄Qn2)=(2-1.^6)

An3 of -⅄(φn4-1⅄Qn3)=(1.5-1.4)

An4 of -⅄(φn5-1⅄Qn4)=(1.^6-1.^571428)

An5 of -⅄(φn6-1⅄Qn5)=(1.6-1.^18)

An6 of -⅄(φn7-1⅄Qn6)=(1.625-1.^307692)

An7 of -⅄(φn8-1⅄Qn7)=(1.^615384-1.^1176470588235294)

An8 of -⅄(φn9-1⅄Qn8)=(1.^619047-1.^210526315789473684)

so if A of -⅄(φn2-1⅄Qn1)cn 

and 

A of -⅄(φn2-2⅄Qn1)cn

then

An1 of -⅄(φn2-2⅄Qn1)=(1-0.^6)

An2 of -⅄(φn3-2⅄Qn2)=(2-0.6)

An3 of -⅄(φn4-2⅄Qn3)=(1.5-0.^714285)

An4 of -⅄(φn5-2⅄Qn4)=(1.^6-0.^63)

An5 of -⅄(φn6-2⅄Qn5)=(1.6-0.^846153)

An6 of -⅄(φn7-2⅄Qn6)=(1.625-0.^7647058823529411)

An7 of -⅄(φn8-2⅄Qn7)=(1.^615384-0.^894736842105263157)

An8 of -⅄(φn9-2⅄Qn8)=(1.^619047-0.^8260869565217391304347)

B=∈2⅄(φn1/Θn2)cn

Bn1=(φn1/Θn2)=(0/1)=0

Bn2=(φn2/Θn3)=(1/0.5)

Bn3=(φn3/Θn4)=(2/0.^6) and Bn3=(φn3/Θn4c2)=(2/0.^66) and Bn3=(φn3/Θn4c3)=(2/0.^666) and so on for variants of ncn 

Bn4=(φn4/Θn5)=(1.5/0.6)

Bn5=(φn5/Θn6)=(1.^6/0.625)

Bn6=(φn6/Θn7)=(1.6/0.^615384)

Bn7=(φn7/Θn8)=(1.625/0.^619047)

Bn8=(φn8/Θn9)=(1.^615384/0.6^1764705882352941)

Bn9=(φn9/Θn10)=(1.^619047/0.6^18)

Bn10=(φn10/Θn11)=(1.6^1762941/0.^6179775280878651685393258764044943820224719101123595505)

Bn11=(φn11/Θn12)=(1.6^18/0.6180^5)

Bn12=(φn12/Θn13)=(1.^61797752808988764044943820224719101123595505/0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566)

Bn13=(φn13/Θn14)=(1.6180^5/0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)

Bn14=(φn14/Θn15)=(1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/0.6^18032786885245901639344262295081967213114754098360655737749)

Bn15=(φn15/Θn16)=(1.6183^0223896551724135014/0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)

Bn16=(φn16/Θn17)=(1.618^032786885245901639344262295081967213114754098360655737704918/0.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)

Bn17=(φn17/Θn18)=(1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843/0.618^034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)

Bn18=(φn18/Θn19)=(1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.^618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)

Bn19=(φn19/Θn20)=(1.6180340557314241486068^11145510835913312693/0.6^1803399852)

Bn20=(φn20/Θn21)=(1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/0.6^180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)

Bn21=(φn21/Θn22)=(1.6^1803399852/0.^618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)

and so on for ∈Bn1=2⅄(φn1/Θn2)ncn equations beyond Bn21 that differs from equations such as ∈Bn1of 2⅄(2φn1/2Θn2)ncn or ∈Bn1of 2⅄(1φn1/2Θn2)ncn and ∈Bn1of 2⅄(2φn1/1Θn2)ncn of ∈2⅄ᐱB(nφncn/nΘncn) sets

C=Ncn 

C is a number of cycles in a repeating decimal stem variant potential 

D=∈1⅄(φn2/Θn1)cn

Dn1=(φn2/Θn1)=(1/0)=0

Dn2=(φn3/Θn2)=(2/1)=2

Dn3=(φn4/Θn3)=(1.5/0.5)=3

Dn4=(φn5/Θn4)=(1.^6/0.^6) ↓ and Dn4=(φn5c2/Θn4)=(1.^66/0.^6) and Dn4=(φn5/Θn4c2)=(1.^6/0.^66) and Dn4=(φn5c2/Θn4c2)=(1.^66/0.^66) and so on for cn 

Dn5=(φn6/Θn5)=(1.6/0.6)=2.^6 or 2.6 or 2.66 or 2.666 and so on

Dn6=(φn7/Θn6)=(1.625/0.625)=2.6

Dn7=(φn8/Θn7)=(1.^615384/0.^615384)=2.^625001 or 2.625001

Dn8=(φn9/Θn8)=(1.^619047/0.^619047)=2.^615386230770846155461540076924692309307693923078538463153847769232384617000001 or 2.615386230770846155461540076924692309307693923078538463153847769232384617000001

Dn9=(φn10/Θn9)=(1.6^1762941/0.6^1764705882352941) with a quotient potential of 61,764,705,882,352,941 digits long to divisor of cn of variable Θn9 of Dn9 and Dn8=(φn9c1/Θn8c2), Dn8=(φn9c2/Θn8c2) each have quotients based on cn of Dn variables φncn/Θncn

Dn10=(φn11/Θn10)=(1.6^18/0.6^18)=2.^6181229773462783171521035598705501 or 2.6181229773462783171521035598705501

Dn11=(φn12/Θn11)=(1.^61797752808988764044943820224719101123595505/0.^6179775280878651685393258764044943820224719101123595505)

Dn12=(φn13/Θn12)=(1.6180^5/0.6180^5)

Dn13=(φn14/Θn13)=(1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566)

Dn14=(φn15/Θn14)=(1.6183^0223896551724135014/0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257)

Dn15=(φn16/Θn15)=(1.618^032786885245901639344262295081967213114754098360655737704918/0.6^18032786885245901639344262295081967213114754098360655737749)

Dn16=(φn17/Θn16)=(1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843/0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870)

Dn17=(φn18/Θn17)=(1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/0.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)

Dn18=(φn19/Θn18)=(1.6180340557314241486068^11145510835913312693/0.618^034055727554179566563467492260061919504643962848297213622291021671826625386996904024767801857585139318885448916408668730650154798761609907120743)

Dn19=(φn20/Θn19)=(1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/0.^618033963166706529538387945467591485290600334848122458741927768476441042812724228653432193255202104759626883520688830423343697679980865821573786175556087060511839272901219803874671131308299449892370246352547237502989715379095910069361396795025113609184405644582635733078210954317149007414494140157856972016264051662281750777325998564936)

Dn20=(φn21/Θn20)=(1.6^1803399852/0.6^1803399852)

Dn21=(φn22/Θn21)=(1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/0.6^180339850173579389731408733784030696144710396491869175954686643522748035812168828795907180705280467750776539375114196966928558377489493879042572629270966563128083318107071076192216334734149460990316097204458249588890919057189841037822035446738534624520372738900054814544125708021194957061940434862050063950301479992691394116572263840672391741275351726658139959802667641147451123698154577014434496619769778914672026310981)

Dn22=(φn23/Θn22)=(1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^96792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/0.^618033990175597086556377392580881937778781548190390153012252272598949805205804302410931059793348766303427248602563378691208853255039241149568065044322737281915193947264411947377336118796228332674609000056462085709446106939190333690926542826492010614872113375868104567782733894190051380497995595957314663203658743153972107729659533623172039975156682287843712946756253175992321156343515329456270114)

and so on for ∈Dn=1⅄(φ/Θ)ncn equations beyond Dn22 that differs from equations such as ∈Dn1of 1⅄(2φn2/2Θn1)ncn or ∈Dn1of 1⅄(1φn2/2Θn1)ncn and ∈Dn1of 1⅄(2φn2/1Θn1)ncn of ∈1⅄ᐱD(nφncn/nΘncn) sets

Given E=∈1⅄(Θ/Q)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so 

E=∈1⅄(Θn2/1⅄Qn1)cn

and

E=∈1⅄(Θn2/2⅄Qn1)cn

then

En1 of 1⅄(Θn2/1⅄Qn1)=(1/1.5)

En2 of 1⅄(Θn3/1⅄Qn2)=(0.5/1.^6)

En3 of 1⅄(Θn4/1⅄Qn3)=(0.^6/1.4)

En4 of 1⅄(Θn5/1⅄Qn4)=(0.6/1.^571428)

En5 of 1⅄(Θn6/1⅄Qn5)=(0.625/1.^18)

En6 of 1⅄(Θn7/1⅄Qn6)=(0.^615384/1.^307692)

En7 of 1⅄(Θn8/1⅄Qn7)=(0.^619047/1.^1176470588235294)

En8 of 1⅄(Θn9/1⅄Qn8)=(0.6^1764705882352941/1.^210526315789473684)

if E=∈1⅄(Θn2/1⅄Qn1)cn

and

E=∈1⅄(Θn2/2⅄Qn1)cn

then

En1 of 1⅄(Θn2/2⅄Qn1)=(1/0.^6)

En2 of 1⅄(Θn3/2⅄Qn2)=(0.5/0.6)

En3 of 1⅄(Θn4/2⅄Qn3)=(0.^6/0.^714285)

En4 of 1⅄(Θn5/2⅄Qn4)=(0.6/0.^63)

En5 of 1⅄(Θn6/2⅄Qn5)=(0.625/0.^846153)

En6 of 1⅄(Θn7/2⅄Qn6)=(0.^615384/0.^7647058823529411)

En7 of 1⅄(Θn8/2⅄Qn7)=(0.^619047/0.^894736842105263157)

En8 of 1⅄(Θn9/2⅄Qn8)=(0.6^1764705882352941/0.^8260869565217391304347)

Given F=∈2⅄(Θ/Q)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so

F=∈2⅄(Θn1/1⅄Qn2)cn

and

F=∈2⅄(Θn1/2⅄Qn2)cn

then

Fn1 of 2⅄(Θn1/1⅄Qn2)=(0/1.^6)

Fn2 of 2⅄(Θn2/1⅄Qn3)=(1/1.4)

Fn3 of 2⅄(Θn3/1⅄Qn4)=(0.5/1.^571428)

Fn4 of 2⅄(Θn4/1⅄Qn5)=(0.^6/1.^18)

Fn5 of 2⅄(Θn5/1⅄Qn6)=(0.6/1.^307692)

Fn6 of 2⅄(Θn6/1⅄Qn7)=(0.625/1.^1176470588235294)

Fn7 of 2⅄(Θn7/1⅄Qn8)=(0.^615384/1.^210526315789473684)

if F=∈2⅄(Θn1/1⅄Qn2)cn

and

F=∈2⅄(Θn1/2⅄Qn2)cn

then

Fn1 of 2⅄(Θn1/2⅄Qn2)=(0/0.6)

Fn2 of 2⅄(Θn2/2⅄Qn3)=(1/0.^714285)

Fn3 of 2⅄(Θn3/2⅄Qn4)=(0.5/0.^63)

Fn4 of 2⅄(Θn4/2⅄Qn5)=(0.^6/0.^846153)

Fn5 of 2⅄(Θn5/2⅄Qn6)=(0.6/0.^7647058823529411)

Fn6 of 2⅄(Θn6/2⅄Qn7)=(0.625/0.^894736842105263157)

Fn7 of 2⅄(Θn7/2⅄Qn8)=(0.^615384/0.^8260869565217391304347)

G=∈2⅄(Θn1/φn2)cn

Gn1=(Θn1/φn2)=(0/1)=0

Gn2=(Θn2/φn3)=(1/2)=0.5

Gn3=(Θn3/φn4)=(0.5/1.5)

Gn4=(Θn4/φn5)=(0.^6/1.^6) and Gn4=(Θn4c2/φn5)=(0.^66/1.^6) and Gn4=(Θn4/φn5c2)=(0.^6/1.^66) and Gn4=(Θn4c2/φn5c2)=(0.^66/1.^66) and so on for variants of ncn

Gn5=(Θn5/φn6)=(0.6/1.6)

Gn6=(Θn6/φn7)=(0.625/1.625)

Gn7=(Θn7/φn8)=(0.^615384/1.^615384)

Gn8=(Θn8/φn9)=(0.^619047/1.^619047)

Gn9=(Θn9/φn10)=(0.6^1764705882352941/1.6^1762941)

Gn10=(Θn10/φn11)=(0.6^18/1.6^18)

Gn11=(Θn11/φn12)=(0.^6179775280878651685393258764044943820224719101123595505/1.^61797752808988764044943820224719101123595505)

Gn12=(Θn12/φn13)=(0.6180^5/1.6180^5)

Gn13=(Θn13/φn14)=(0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566/1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)

Gn14=(Θn14/φn15)=(0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/1.6183^0223896551724135014)

Gn15=(Θn15/φn16)=(0.6^18032786885245901639344262295081967213114754098360655737749/1.618^032786885245901639344262295081967213114754098360655737704918)

Gn16=(Θn16/φn17)=(0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843)

and so on for ∈Gn=2⅄(Θ/φ)ncn

Given H=∈2⅄(Q/Θ)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so

H=∈2⅄(1⅄Qn1/Θn2)cn

and

H=∈2⅄(2⅄Qn1/Θn2)cn

then

Hn1 of 2⅄(1⅄Qn1/Θn2)=(1.5/1)

Hn2 of 2⅄(1⅄Qn2/Θn3)=(1.^6/0.5)

Hn3 of 2⅄(1⅄Qn3/Θn4)=(1.4/0.^6)

Hn4 of 2⅄(1⅄Qn4/Θn5)=(1.^571428/0.6)

Hn5 of 2⅄(1⅄Qn5/Θn6)=(1.^18/0.625)

Hn6 of 2⅄(1⅄Qn6/Θn7)=(1.^307692/0.^615384)

Hn7 of 2⅄(1⅄Qn7/Θn8)=(1.^1176470588235294/0.^619047)

Hn8 of 2⅄(1⅄Qn8/Θn9)=(1.^210526315789473684/0.6^1764705882352941)

then

if H=∈2⅄(1⅄Qn1/Θn2)cn

and

H=∈2⅄(2⅄Qn1/Θn2)cn

then

Hn1 of 2⅄(2⅄Qn1/Θn2)=(0.^6/1)

Hn2 of 2⅄(2⅄Qn2/Θn3)=(0.6/0.5)

Hn3 of 2⅄(2⅄Qn3/Θn4)=(0.^714285/0.^6)

Hn4 of 2⅄(2⅄Qn4/Θn5)=(0.^63/0.6)

Hn5 of 2⅄(2⅄Qn5/Θn6)=(0.^846153/0.625)

Hn6 of 2⅄(2⅄Qn6/Θn7)=(0.^7647058823529411/0.^615384)

Hn7 of 2⅄(2⅄Qn7/Θn8)=(0.^894736842105263157/0.^619047)

Hn8 of 2⅄(2⅄Qn8/Θn9)=(0.^8260869565217391304347/0.6^1764705882352941)

Given I= ∈1⅄(Q/Θ)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so

I= ∈1⅄(1⅄Qn2/Θn1)cn

and

I= ∈1⅄(2⅄Qn2/Θn1)cn

then

In1 of 1⅄(1⅄Qn2/Θn1)=(1.^6/0)

In2 of 1⅄(1⅄Qn3/Θn2)=(1.4/1)

In3 of 1⅄(1⅄Qn4/Θn3)=(1.^571428/0.5)

In4 of 1⅄(1⅄Qn5/Θn4)=(1.^18/0.^6)

In5 of 1⅄(1⅄Qn6/Θn5)=(1.^307692/0.6)

In6 of 1⅄(1⅄Qn7/Θn6)=(1.^1176470588235294/0.625)

In7 of 1⅄(1⅄Qn8/Θn7)=(1.^210526315789473684/0.^615384)

if I= ∈1⅄(1⅄Qn2/Θn1)cn

and

I= ∈1⅄(2⅄Qn2/Θn1)cn

then

In1 of 1⅄(2⅄Qn2/Θn1)=(0.6/0)

In2 of 1⅄(2⅄Qn3/Θn2)=(0.^714285/1)

In3 of 1⅄(2⅄Qn4/Θn3)=(0.^63/0.5)

In4 of 1⅄(2⅄Qn5/Θn4)=(0.^846153/0.^6)

In5 of 1⅄(2⅄Qn6/Θn5)=(0.^7647058823529411/0.6)

In6 of 1⅄(2⅄Qn7/Θn6)=(0.^894736842105263157/0.625)

In7 of 1⅄(2⅄Qn8/Θn7)=(0.^8260869565217391304347/0.^615384)

Given J=∈2⅄(2⅄Qn1/1⅄Qn2)cn

∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2)=(0.^6/1.^6) 

depending of cn variable factor and are crossed variants of two different path sets variables 

then

Jn1=∈2⅄2Qn1 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn1/1⅄1Qn2)=(0.^6/1.^6)

Jn2=∈2⅄2Qn2 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn2/1⅄1Qn3)=(0.6/1.4)

Jn3=∈2⅄2Qn3 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn3/1⅄1Qn4)=(0.^714285/1.^571428)

Jn4=∈2⅄2Qn4 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn4/1⅄1Qn5)=(0.^63/1.^18)

Jn5=∈2⅄2Qn5 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn5/1⅄1Qn6)=(0.^846153/1.^307692)

Jn6=∈2⅄2Qn6 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn6/1⅄1Qn7)=(0.^7647058823529411/1.^1176470588235294)

Jn7=∈2⅄2Qn7 of ∈2⅄1Qn and ∈1⅄1Qn variables is (2⅄1Qn7/1⅄1Qn8)=(0.^894736842105263157/1.^210526315789473684)

Variable Factor 2⅄2Qnc1 will differ variants of ∈2⅄1Qn and ∈1⅄1Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .

Given K=∈2⅄(1⅄Qn1/2⅄Qn2)cn

∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2)=(1.5/0.6) depending of cn variable factor

then

Kn1=∈2⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn1/2⅄1Qn2)=(1.5/0.6)

Kn2=∈2⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn3)=(1.^6/0.^714285)

Kn3=∈2⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn3/2⅄1Qn4)=(1.4/0.^63)

Kn4=∈2⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn4/2⅄1Qn5)=(1.^571428/0.^846153)

Kn5=∈2⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn5/2⅄1Qn6)=(1.^18/0.^7647058823529411)

Kn6=∈2⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn6/2⅄1Qn7)=(1.^307692/0.^894736842105263157)

Kn7=∈2⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn7/2⅄1Qn8)=(1.^1176470588235294/0.^8260869565217391304347)

Variable Factor 2⅄2Qnc1 will differ variants of ∈1⅄1Qn and ∈2⅄1Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .

Given L=∈1⅄(1⅄Qn2/2⅄Qn1)cn

∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.^6/0.^6)=2.^6 depending of cn variable factor c1

then

Ln1=∈1⅄2Qn1 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn2/2⅄1Qn1)=(1.^6/0.^6)=2.^6

Ln2=∈1⅄2Qn2 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn3/2⅄1Qn2)=(1.4/0.6)

Ln3=∈1⅄2Qn3 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn4/2⅄1Qn3)=(1.^571428/0.^714285)

Ln4=∈1⅄2Qn4 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn5/2⅄1Qn4)=(1.^18/0.^63)

Ln5=∈1⅄2Qn5 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn6/2⅄1Qn5)=(1.^307692/0.^846153)

Ln6=∈1⅄2Qn6 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn7/2⅄1Qn6)=(1.^1176470588235294/0.^7647058823529411)

Ln7=∈1⅄2Qn7 of ∈1⅄1Qn and ∈2⅄1Qn variables is (1⅄1Qn8/2⅄1Qn7)=(1.^210526315789473684/0.^894736842105263157)

Variable Factor 1⅄2Qnc1 will differ variants of ∈1⅄2Qn given a factor 1⅄1Qnc2 factor 2⅄1Qnc2 and so on . . .

Given M=∈2⅄(φ/Q)cn

The definition of Q variable should be accurate to its defining base path where 1⅄Q and 2⅄Q, differ from prime base just as φ and Θ differ in paths 1⅄ and 2⅄ of Y base.

so

M=∈2⅄(φn1/1⅄Qn2)cn

and

M=∈2⅄(φn1/2⅄Qn2)cn

then

Mn1 of ∈2⅄(φn1/1⅄Qn2)=(0/1.^6)

Mn2 of ∈2⅄(φn2/1⅄Qn3)=(1/1.4)

Mn3 of ∈2⅄(φn3/1⅄Qn4)=(2/1.^571428)

Mn4 of ∈2⅄(φn4/1⅄Qn5)=(1.5/1.^18)

Mn5 of ∈2⅄(φn5/1⅄Qn6)=(1.^6/1.^307692)

Mn6 of ∈2⅄(φn6/1⅄Qn7)=(1.6/1.^1176470588235294)

Mn7 of ∈2⅄(φn7/1⅄Qn8)=(1.625/1.^210526315789473684)

if M=∈2⅄(φn1/1⅄Qn2)cn

and

M=∈2⅄(φn1/2⅄Qn2)cn

then

Mn1 of ∈2⅄(φn1/2⅄Qn2)=(0/0.6)

Mn2 of ∈2⅄(φn2/2⅄Qn3)=(1/0.^714285)

Mn3 of ∈2⅄(φn3/2⅄Qn4)=(2/0.^63)

Mn4 of ∈2⅄(φn4/2⅄Qn5)=(1.5/0.^846153)

Mn5 of ∈2⅄(φn5/2⅄Qn6)=(1.^6/0.^7647058823529411)

Mn6 of ∈2⅄(φn6/2⅄Qn7)=(1.6/0.^894736842105263157)

Mn7 of ∈2⅄(φn7/2⅄Qn8)=(1.625/0.^8260869565217391304347)

Nncn 

N is a number and n is the numerated number of a sequence in labeled number scales that C cycles of a decimal numerated consecutive number is labeled to that N number.

As any variable of the ratio scales can be defined as a number to the decimal stem counted degree of sequence repetitions in the decimal cycle count, a number that is not factored from these many computational equations can too also be a number.

4 6 9 10 12 14 15 16 18 20 22 24 25 26 27 28 30 32 33 35 36 38 39 40 42 44 45 46 48 49 50 51 52 54 56 57 58 60 62 63 64 65 66 68 69 70 72 74 75 76 77 78 80 81 82 84 85 86 87 88 90 91 92 93 94 95 96 98 99 100 and so on . . .

These whole numbers are variables that are neither Y base fibonacci numerals nor are they prime numbers and yet these numbers are still factorable numerals of a set entirely different than Y, P, A through Z, φ, and Θ.

In this case we note the set as (N) of Ψ such that psi represents N whole numbers that are not prime nor fibonacci based numerals and are an ordinal set of consecutive values.

N then is a number and N represents any number of any set including numbers that can not be defined to any of these sets.

A  B  D  E  F  G  H  I  J  K  L  M  O  P  Q  R  S  T  U  V  W  X  Y  Z  φ  Θ  ᐱ  ᗑ  ∘⧊°  ∘∇°  ∀

As C cycles of repeating ratios are numerable then cn or CN is a cycle count of N many cycle counts that its self can be whole and partial of...

O=∈1⅄(Θn2/φn1)cn

On1=(Θn2/φn1)=(1/0)=0

On2=(Θn3/φn2)=(0.5/1)

On3=(Θn4/φn3)=(0.^6/2) and On3=(Θn4c2/φn3)=(0.^66/2) and On3=(Θn4c3/φn3)=(0.^666/2) and so on for variants of ncn

On4=(Θn5/φn4)=(0.6/1.5)

On5=(Θn6/φn5)=(0.625/1.^6)

On6=(Θn7/φn6)=(0.^615384/1.6)

On7=(Θn8/φn7)=(0.^619047/1.625)

On8=(Θn9/φn8)=(0.6^1764705882352941/1.^615384)

On9=(Θn10/φn9)=(0.6^18/1.^619047)

On10=(Θn11/φn10)=(0.^6179775280878651685393258764044943820224719101123595505/1.6^1762941)

On11=(Θn12/φn11)=(0.6180^5/1.6^18)

On12=(Θn13/φn12)=(0.6180257553648064377682403433476394849785407725322060085836909871244635193133047210300429184^54935622317596566/1.^61797752808988764044943820224719101123595505)

On13=(Θn14/φn13)=(0.610079575596814323607427055702917771827585941644562334217506631^294429708196286206893896551724137931034482493368673740053050397875331564986472148514588567639257/1.6180^5)

On14=(Θn15/φn14)=(0.6^18032786885245901639344262295081967213114754098360655737749/1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)

On15=(Θn16/φn15)=(0.^618034447821681864235055724417426545086119554204660587639311043566362715298885511651469098277608915906788247213779128672745684022289766870/1.6183^0223896551724135014)

and so on for ∈On=1⅄(Θ/φ)cn

2 

3 

5 

7 

11 

13 

17 

19 

23

29

31 

37 

41 

43 

47 

53 

59 

61 

67 

71 

73 

79 

83 

89 

97 

101 

103 

107 

109 

113 

127 

131 

137 

139 

149 

151 

157 

163 

167 

173 

179 

181 

191 

193 

197 

199 

Q represents a ratio of prime divided by prime

Q=(⅄p/⅄p) so ∈1⅄Q=(Pn2/Pn1) and ∈2⅄Q=(Pn1/Pn2)

Given R=∈(φ/P)cn

R represents ∈(φ/P)cn

3⅄φncn/pn that path 3⅄ of φncn/pn  differ from paths 2⅄φncn/pn and 1⅄φncn/pn

Path 3⅄R=φn1cn/pn1

3⅄Rn1=1φn1/pn1=(φn1/pn1)=(0/2)=0 

3⅄Rn2=1φn2/pn2=∈(φn2/pn2)=(1/3)=0.^3

3⅄Rn3=1φn3/pn3=(φn3/pn3)=(2/5)=0.4

3⅄Rn4=1φn4/pn4=∈(φn4/pn4)=(1.5/7)=0.2^142857

3⅄Rn5=1φn5/pn5=∈(φn5/pn5)=(1.^6/11)=1.^45→. . .(φn5c2/pn5)=(1.^66/11)=0.150^9→. . . and so on

3⅄Rn6=1φn6/pn6=∈(φn6/pn6)=(1.6/13)=0.1^230769

3⅄Rn7=1φn7/pn7=∈(φn7/pn7)=(1.625/17)=0.095^5882352941176470 

3⅄Rn8=1φn8/pn8=∈(φn8/pn8)=(1.^615384/19)=0.079757^052631578421→. . .(φn8c2/pn8)=0.079757079757^052631578421→. . . and so on

3⅄Rn9=1φn9/pn9=∈(φn9/pn9)=(1.^619047/23)=0.070393^3478260865217391304

Path 1⅄R=φn2/pn1

1⅄Rn1=(φn2/pn1)=(1/2)

1⅄Rn2=(φn3/pn2)=(2/3)

1⅄Rn3=(φn4/pn3)=(1.5/5)

1⅄Rn4=(φn5/pn4)=(1.^6/7)

1⅄Rn5=(φn6/pn5)=(1.6/11)

1⅄Rn6=(φn7/pn6)=(1.625/13)

1⅄Rn7=(φn8/pn7)=(1.^615384/17)

1⅄Rn8=(φn9/pn8)=(1.^619047/19)

1⅄Rn9=(φn10/pn9)=(1.6^1762941/23)

Path 2⅄R=φn1/pn2

2⅄Rn1=(φn1/pn2)=(0/3)

2⅄Rn2=(φn2/pn3)=(1/5)

2⅄Rn3=(φn3/pn4)=(2/7)

2⅄Rn4=(φn4/pn5)=(1.5/11)

2⅄Rn5=(φn5/pn6)=(1.^6/13)

2⅄Rn6=(φn6/pn7)=(1.6/17)

2⅄Rn7=(φn7/pn8)=(1.625/19)

2⅄Rn8=(φn8/pn9)=(1.^615384/23)

S=∈(P/Θ)cn

S represents ∈(P/Θ)cn

3⅄Pn1/Θn1cn that path 3⅄ of Pn1/Θn1cn  differ from paths 2⅄Pn1/Θn2cn and 1⅄Pn2/Θn1cn based on cn of theta Θn variable and variable of the sequential set with no steps

Path 1⅄S=Pn2/Θn1cn

1⅄Sn1=Pn2/Θn1cn=(Pn2/Θn1cn)=(3/0)=0

1⅄Sn2=Pn3/Θn2cn=(Pn3/Θn2cn)=(5/1)=5

1⅄Sn3=Pn4/Θn3cn=(Pn4/Θn3cn)=(7/0.5)=14

1⅄Sn4=Pn5/Θn4cn=(Pn5/Θn4c1)=(11/0.^6)=18.^3 or 18.3 and 1⅄Sn4=Pn5/Θn4cn=(Pn5/Θn4c2)=(11/0.^66)=18.^6 or 18.6 and so on for cn variants of 1⅄Sn4 

1⅄Sn5=Pn6/Θn5cn=(Pn6/Θn5cn)=(13/0.6)=21.^6 or 21.6

1⅄Sn6=Pn7/Θn6cn=(Pn7/Θn6cn)=(17/0.625)=27.2

1⅄Sn7=Pn8/Θn7cn=(Pn8/Θn7cn)=(19/0.^615384)=^30.8750 or 30.8750308750

1⅄Sn8=Pn9/Θn8cn=(Pn9/Θn8cn)=(23/0.^619047)=^37.1538833077294615756154217692679231140769602308063846525384986923448461910000371538833077294615756154217692679231140769602308063846525384986923448461910000 

or

37.1538833077294615756154217692679231140769602308063846525384986923448461910000371538833077294615756154217692679231140769602308063846525384986923448461910000371538833077294615756154217692679231140769602308063846525384986923448461910000371538833077294615756154217692679231140769602308063846525384986923448461910000

1⅄Sn9=Pn10/Θn9cn=(Pn10/Θn9cn)=(29/0.6^1764705882352941)=46.9523809523809525151020408163265309955296404275996123681799 extended shell continues with a quotient decimal stem cycle potential having the probability based on divisor or 61,764,705,882,352,941 or less digits determined by this cn variable

1⅄Sn10=Pn11/Θn10cn=(Pn11/Θn10cn)=(31/0.6^18)=^50.16181229773462783171521035598705 or 50.1618122977346278317152103559870550.16181229773462783171521035598705 and so on . . . for 1⅄Sn10c1, 1⅄Sn10c2, 1⅄Sn10c3 infinitely

and so on for cn variables of ∈1⅄Sn

Path 2⅄S=Pn1/Θn2cn

2⅄Sn1=Pn1/Θn2cn=(Pn1/Θn2cn)=(2/1)=2

2⅄Sn2=Pn2/Θn3cn=(Pn2/Θn3cn)=(3/0.5)=6

2⅄Sn3=Pn3/Θn4cn=(Pn3/Θn4cn)=(5/0.^6)=8.^3 or 8.3

2⅄Sn4=Pn4/Θn5cn=(Pn4/Θn5cn)=(7/0.6)=11.^6 or 11.6 or 11.66 or 11.666 and so on

2⅄Sn5=Pn5/Θn6cn=(Pn5/Θn6cn)=(11/0.625)=17.6

2⅄Sn6=Pn6/Θn7cn=(Pn6/Θn7cn)=(13/0.^615384)=^21.1250 or 21.1250211250 and so on . . . 2⅄Sn6c1, 2⅄Sn6c2, 2⅄Sn6c3  infinitely

while 2⅄Sn6=Pn6/Θn7c2=(13/0.^615384615384)=^21.1250000000 or 21.1250000000211250000000 and so on . . .