General Locus for differentiation

== The problem of differential equations ==
The problem of differential equations is - "cyclic redemption" with the consideration that there weren't any z axis. Or it that when there is x,y axis it is always that z axis is implicit with unit 1.

It is known that point lies on the circle (x,y) represented by (rCosθ,rSinθ).

By that we can say
x=rCosθ
y=rSinθ

In nature, we cannot find anything perfect as circle or sphere, but it is almost to it. Having that we can say,

x=rCosθ+Δx
y=rSinθ+Δy

x/y=rCosθ+Δx/rSinθ+Δy

To avoid abnormalities consider x/y=1 as z=1 so its equality is maintained. See, NP₀ = 1. Sinθ/θ = 1 when θ tends to 0.

rCosθ+Δx/rSinθ+Δy=1

rCosθ+Δx/rSinθ+Δy=1

rCosθ+Δx=rSinθ+Δy

Δy=rCosθ+Δx-rSinθ

Δy/Δx=[rCosθ/Δx]+[1]-[rSinθ/Δx]

Δy/Δx=[(rCosθ-rSinθ)/Δx]+1

Δy/Δx=[rCosθ+Δx-rSinθ/Δx]

[Δy=rCosθ+Δx-rSinθ]

'''When you say dy then it is that,'''

dy=y+Δy

dy=y+rCosθ+Δx-rSinθ [as x=rCosθ, y=rSinθ So,] [or logical plane z=1]

dy=y+x+Δx-y

dy=x+Δx

as dx=x+Δx so

[dy=dx]

=== The General Equality Locus of differentiation is ===
dy=dx when plane-z=1, if it is not (z!=1) this equality is accords. So it is not dy/dx gives some ratio rather, make it dy=dx leverage with z-plane analysis like 1,NP_r series.

This will avoid cyclic redemption problem of differentiation that it is ignoring that there is a z-axis

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Ref:

https://en.wikipedia.org/wiki/Group_structure_and_the_axiom_of_choice
http://en.wikipedia.org/wiki/Talk:Derivative#The_problem_of_differential_equations