User talk:Sven.st

This looks like a proof around a deleted neighborhood.

If, naively, I took the function expression Gi(Ai)=(Bi). I would read this as a proof of proportionality. y=kx

Why could I not rearrange to Gi=(Bi)/(Ai)

In addition if in n≥3

we multiply by unity in the form of 6/6 along the set of n

and arrive at 18/6, 24/6, 30/6, 36/6 and so on

Grouping these in bundles of three, so 18/6 becomes 3 groups of 6 gons, 24/6 becomes 4 groups of 6 gons, 30/6 becomes 5 groups of 6 gons and so on. The numerator labels the circle, each distinct.

By bounding out 1 and 2 we removed parity by bounding out the origin. We return to parity by multiplying by unity in 6/6. Factored as 2*3.

We can then translate and rotate in a very specific ways. Along the surface in translation and and proportionately by multiples of the radius of curvature.

Since n is positive and ascending, I read the resulting spheres as concave always. The spheres second half is mapped to the rear surface of it's front half. Each surface is modeled as a radius of curvature. Any n makes a distinct sphere. It translates around a corkscrew spiral which visits every surface in order from n=3.

I am a layman too so take everything I say with a grain of salt and consider asking on the talk page of the article, if you still have questions.

First I want to make sure we are talking about the same thing: You seem to be referring to my edit on the Banach–Tarski paradox.

So $A_{i}$ and $B_{i}$ are subsets of a set $X$ and $g_{i}$ is an element of some group $G$.

I am not very experienced with group theory so I prefer to just think about the common special case mentioned in the article, where $X$ is an $n$-dimensional Euclidean space and $G$ is the group of all isometries of $X$(so $A_{i},B_{i}$ are sets of points and $g_{i}$ is a transformation composed of translation, rotation and/or reflection).

In my understanding the formula $g_{i}(A_{i})=B_{i}$ does therefore not mean that $g_{i}$ gets multiplied by $A_{i}$, but that the action of $g_{i}$ is applied to $A_{i}$.

If you look at the equation this way you will notice that you can not rearrange it by dividing both sides by $A_{i}$ just like you can not rearrange $\sin(x)=y$ to $\sin ={\frac {y}{x}}$. In addition to that "dividing" by $A_{i}$ is not even defined, because $A_{i}$ is not a number, but a set of points.

I don't think it is right to say, that $g_{i}(A_{i})=B_{i}$ means that $A_{i}$s and $B_{i}$s are proportional (i.e. they can be transformed into each other by multiplication with a constant factor), but that they are congruent(i.e. they can be transformed into each other by a length-preserving transformation).

I did not understand the second part of your question completely, maybe you can phrase it in a different way and clarify a few points? $n$ is the dimension of the Euclidian space $X$? Then n is surely positive, but why should it be "ascending"? What do you want to multiply by 6/6? All possible dimensions $n$? I am not sure why the Banach-Tarski-Paradox should be related to deleted neighbourhoods, what exactly looks similar to which proof involving deleted neighbourhoods?

PS: According to Wikipedia:Signatures#When signatures should and should not be used you should add a signature to your posts to talk pages by appending four tilde characters ~~~~ to it. Also if you use a heading then it is easier to see to which discussion a post belongs.

Sven.st (talk) 18:10, 22 August 2017 (UTC)