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1 decimal integer ring cycle of many
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Exponential arc path functions dependent of definition of cn and ratio value where applicable with fractals to being the multiple of the number from some complex and basic numerals.
Multiplication after division, what is an error in order of operations to PEMDAS with many of these variables.
Variables of A B D E F G H I J K L M N O P Q R S T U V W X Y Z φ Θ Ψ ᐱ ᗑ ∘⧊° ∘∇° are applicable to a function.
Function path ⅄ncn=(⅄nncn)(ncn) is nncn to a multiple of nncn such that nncn is a number or variable with a repeating or not repeating decimal stem cycle variant. =
Examples of ⅄ncn=(⅄nncn)(ncn)
⅄ncn=(⅄nncn)(2)=(nncn)x(nncn)
⅄ncn=(⅄nncn)(3)=(nncn)x(nncn)x(nncn)
⅄ncn=(⅄nncn)(10)=(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)
⅄ncnᐱA exponential complex function variables of Ancn
if A=∈1⅄(φ/Q)cn and path ⅄ of Q is a variant in the definition of A then
A=1⅄(φn2/Qn1)=[(Yn2/Yn1)/(P/P) while Q requires path definition of 1⅄Q or 2⅄Q from P two sets of A complete the formula of Q variable.
A=1⅄(φn2/1⅄Qn1)=[(Yn3/Yn2)/(Pn2/Pn1)=(1/1)/(3/2)=(1/1.5)=0.^6
and
A=1⅄(φn2/2⅄Qn1c1)=[(Yn3/Yn2)/(Pn1/Pn2)=(1/1)/(2/3)=(1/0.^6)=1.^6
Applied function of ⅄ncn=(⅄nncn)(ncn) with A variables is then
An1 of 1⅄(φn2/1⅄Qn1)c1 along path ⅄(2)=(1⅄(φn2/1⅄Qn1))c1(1⅄(φn2/1⅄Qn1)c1) or [An1 of 1⅄(φn2/1⅄Qn1)c1 x An1 of 1⅄(φn2/1⅄Qn1)c1]
and
An1 of 1⅄(φn2/2⅄Qn1c1)c1 along path ⅄(2)=(1⅄(φn2/2⅄Qn1c1))c1(1⅄(φn2/2⅄Qn1c1)c1) or [An1 of 1⅄(φn2/2⅄Qn1c1)c1 x An1 of 1⅄(φn2/2⅄Qn1c1)c1]
⅄(2)ᐱAn1=
⅄(2)=(1⅄(φn2/1⅄Qn1))c1(1⅄(φn2/1⅄Qn1)c1)=0.6(2)=0.6x0.6=0.36
and
⅄(2)=(1⅄(φn2/2⅄Qn1c1))c1(1⅄(φn2/2⅄Qn1c1)c1)=1.6(2)=1.6x1.6=2.56
⅄(2)ᐱAn1=
[An1 of 1⅄(φn2/1⅄Qn1)c1 x An1 of 1⅄(φn2/1⅄Qn1)c1]=0.36
and
[An1 of 1⅄(φn2/2⅄Qn1c1)c1 x An1 of 1⅄(φn2/2⅄Qn1c1)c1]=2.56
Any change in cn stem decimal cycle count variable will change the multiple of the exponent squared value in the example and ultimately the final product value also.
Potential Change of An1 of 1⅄(φn2/1⅄Qn1)c1 is An1c1=0.6, An1c2=0.66, An1c3=0.666 and so on for An1 of 1⅄(φn2/1⅄Qn1)
then ⅄(2)ᐱAn1c2 of 1⅄(φn2/1⅄Qn1)=0.66(2)=(0.66x0.66)=0.4356
and ⅄(2)ᐱAn1c3 of 1⅄(φn2/1⅄Qn1)=0.666(2)=(0.666x0.666)=0.443556
Potential Change of An1 of 1⅄(φn2/2⅄Qn1c1)c1 is based at variable 2⅄Qn1cn as well as An1 of 1⅄(φn2/2⅄Qn1c1)cn
if 2⅄Qn1cn for An1 of 1⅄ path (φn2/2⅄Qn1c1) is 2⅄Qn1c2 then A=1⅄(φn2/2⅄Qn1c2)=[(Yn3/Yn2)/(Pn1/Pn2)=(1/1)/(2/3)=(1/0.^66)=^1.5
and ⅄(2)ᐱAn1c1 of 1⅄(φn2/2⅄Qn1c2)=1.5(2)=(1.5x1.5)=2.25 while ⅄(2)ᐱAn1c2 of 1⅄(φn2/2⅄Qn1c2)=1.515(2)=(1.515x1.515)=2.295225
however
A=1⅄(φn2/2⅄Qn1c1)=[(Yn3/Yn2)/(Pn1/Pn2)=(1/1)/(2/3)=(1/0.^6)=1.^6 and ⅄(2)ᐱA of 1⅄(φn2/2⅄Qn1c1)=(1.^6)(2)=(1.6x1.6)=2.56
then ⅄(2)ᐱAn1c2 of 1⅄(φn2/2⅄Qn1c1)(1.^66)(2)=(1.66x1.66)=2.7556 and ⅄(2)ᐱAn1c3 of 1⅄(φn2/2⅄Qn1c1)(1.^666)(2)=(1.666x1.666)=2.775556
It is not that these order of operations are incorrect by any means given the path and extent of the defined variables decimal stem cycles have potential change and limit to the variable definition at cn of the variants.
Although 0.4356 ≠ 0.443556 ≠ 2.25 ≠ 2.295225 ≠ 2.56 ≠ 2.7556 ≠ 2.775556 are not equal.
The values are precise scale variables to the function of ƒ⅄(2)ᐱAn1cn of ∈[0.4356; 0.443556; 2.25; 2.295225; 2.56; 2.7556; 2.775556 . . .} of altered paths with variants Ancn within the paths sub-units n⅄Qncn. These are exponential products from ratios divided by ratios from variables of consecutive bases in y fibonacci and p prime variables.
Commonly referred to as an algorithm of partial derivative quadratic set variables...
Variable change in cn stem decimal cycle count variables, when applied to numbers greater in exponent will produce astronomical differences in numerical precision based products, quotients, sums, and differences.
With Variables of set ∈A complex variables factor to quotients that are applicable to examples of ⅄ncn=(⅄nncn)(ncn)
⅄ncn=(⅄nncn)(2)=(nncn)x(nncn)
⅄ncn=(⅄nncn)(3)=(nncn)x(nncn)x(nncn)
⅄ncn=(⅄nncn)(10)=(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn)x(nncn) with definitions in
∈n⅄ᐱ(An/An), ∈n⅄ᐱ(An/Bn), ∈n⅄ᐱ(An/Dn), ∈n⅄ᐱ(An/En), ∈n⅄ᐱ(An/Fn), ∈n⅄ᐱ(An/Gn), ∈n⅄ᐱ(An/Hn), ∈n⅄ᐱ(An/In), ∈n⅄ᐱ(An/Jn), ∈n⅄ᐱ(An/Kn), ∈n⅄ᐱ(An/Ln), ∈n⅄ᐱ(An/Mn), ∈n⅄ᐱ(An/Nn), ∈n⅄ᐱ(An/On), ∈n⅄ᐱ(An/Pn), ∈n⅄ᐱ(An/Qn), ∈n⅄ᐱ(An/Rn), ∈n⅄ᐱ(An/Sn), ∈n⅄ᐱ(An/Tn),∈n⅄ᐱ(An/Un), ∈n⅄ᐱ(An/Vn), ∈n⅄ᐱ(An/Wn), ∈n⅄ᐱ(An/Yn), ∈n⅄ᐱ(An/Zn), ∈n⅄ᐱ(An/φn), ∈n⅄ᐱ(An/Θn), ∈n⅄ᐱ(An/Ψn), ∈n⅄ᐱ(An/ᐱn), ∈n⅄ᐱ(An/ᗑn), ∈n⅄ᐱ(An/∘⧊°n), ∈n⅄ᐱ(An/∘∇°n)
such that a variable from these sets is applicable to be squared, cubed, factored to the power of 10, and so on with exponential precision based on nncn numbered cycles in ratio decimal stem value. =
Sets ∈A applied to a squared function ⅄ncn=(⅄nncn)(2)
n⅄ncnᐱ(An/An)(2)=(An/An)x(An/An)
n⅄ncnᐱ(An/Bn)(2)=(An/Bn)x(An/Bn)
n⅄ncnᐱ(An/Dn)(2)=(An/Dn)x(An/Dn)
n⅄ncnᐱ(An/En)(2)=(An/En)x(An/En)
n⅄ncnᐱ(An/Fn)(2)=(An/Fn)x(An/Fn)
n⅄ncnᐱ(An/Gn)(2)=(An/Gn)x(An/Gn)
n⅄ncnᐱ(An/Hn)(2)=(An/Hn)x(An/Hn)
n⅄ncnᐱ(An/In)(2)=(An/In)x(An/In)
n⅄ncnᐱ(An/Jn)(2)=(An/Jn)x(An/Jn)
n⅄ncnᐱ(An/Kn)(2)=(An/Kn)x(An/Kn)
n⅄ncnᐱ(An/Ln)(2)=(An/Ln)x(An/Ln)
n⅄ncnᐱ(An/Mn)(2)=(An/Mn)x(An/Mn)
n⅄ncnᐱ(An/Nn)(2)=(An/Nn)x(An/Nn)
n⅄ncnᐱ(An/On)(2)=(An/On)x(An/On)
n⅄ncnᐱ(An/Pn)(2)=(An/Pn)x(An/Pn)
n⅄ncnᐱ(An/Qn)(2)=(An/Qn)x(An/Qn)
n⅄ncnᐱ(An/Rn)(2)=(An/Rn)x(An/Rn)
n⅄ncnᐱ(An/Sn)(2)=(An/Sn)x(An/Sn)
n⅄ncnᐱ(An/Tn)(2)=(An/Tn)x(An/Tn)
n⅄ncnᐱ(An/Un)(2)=(An/Un)x(An/Un)
n⅄ncnᐱ(An/Vn)(2)=(An/Vn)x(An/Vn)
n⅄ncnᐱ(An/Wn)(2)=(An/Wn)x(An/Wn)
n⅄ncnᐱ(An/Yn)(2)=(An/Yn)x(An/Yn)
n⅄ncnᐱ(An/Zn)(2)=(An/Zn)x(An/Zn)
n⅄ncnᐱ(An/φn)(2)=(An/φn)x(An/φn)
n⅄ncnᐱ(An/Θn)(2)=(An/Θn)x(An/Θn)
n⅄ncnᐱ(An/Ψn)(2)=(An/Ψn)x(An/Ψn)
n⅄ncnᐱ(An/ᐱn)(2)=(An/ᐱn)x(An/ᐱn)
n⅄ncnᐱ(An/ᗑn)(2)=(An/ᗑn)x(An/ᗑn)
n⅄ncnᐱ(An/∘⧊°n)(2)=(An/∘⧊°n)x(An/∘⧊°n)
n⅄ncnᐱ(An/∘∇°n)(2)=(An/∘∇°n)x(An/∘∇°n)
And so on for sets ∈A applied to a squared function ⅄ncn=(⅄nncn)(2), ⅄ncn=(⅄nncn)(3), ⅄ncn=(⅄nncn)(10), to ⅄ncn=(⅄nncn)(n)
Variable definition (⅄nncn) decimal stem cycle count is required before any exponential factoring is applied of the variables in exponent path functions.
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