How many regions are created by the set of all hyperplanes defined by a set of points?

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How many regions are created by the set of all hyperplanes defined by a set of points?

If we have a set of points X in d-dimensional euclidean space, and we look at the set of all n-dimensional hyperplanes that are defined by any subset Y of X (in the sense of being the unique n-dimensional hyperplane containing the points of Y), ranging over all Y in P(X), is there a result for the number of regions defined by this hyperplane arrangement? edit: I just realized, I'm not sure this makes sense for arbitrary n, only n=d-1.

Answer:

I will recast the question as how many pieces can $d$ dimensional space be cut into by $n$ $d-1$ dimensional...

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user114766 at Mathematics Mark as irrelevant Undo

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Some members are thorough in psychology and more members does not have. There is one psychology category...

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Rawrr Reptar its Hannah at Yahoo! Answers Mark as irrelevant Undo

Why does set.begin() return 0?

I have created a structure: struct nod { short place, val; int dist; bool operator< (const nod a) const { return this->val < a.val; } }; Then I have created a set of this structure: set< nod > coada; I made sure I inserted MORE THAN 1...

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set is an ordered unique container. It needs a way to determine both order, and uniqeness. It needs...

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repp4rad... at Yahoo! Answers Mark as irrelevant Undo

Answer:

By "one set of points" I'm guessing you mean you have at least 2 points. The first thing you...

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*questions* at Yahoo! Answers Mark as irrelevant Undo

Let A be a nonempty subset and let B be a fixed subset of A. A relation R defined on the set of subsets of A is defined by XRY if X intersec?

Let A be a nonempty subset and let B be a fixed subset of A. A relation R defined on the set of subsets of A is defined by X RY if (X intersects B) = (Y intersects B) (a) Prove that ...show more

Answer:

Let A be a nonempty subset of what?

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NAQLVG6EDRW7W2U622OXDBN32I at Yahoo! Answers Mark as irrelevant Undo

Do PSN points need to be bought in the country where the account is set?

In my 360, my account had been created with an email with country/region set to USA. Because of that, my account only accepted microsoft points bought in USA. Points I bought in other countries were useless. Does the same thing happen with PSN points...

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Yes, you can only add wallet funds from PSN cards/credit cards in the local currency, so a UK account...

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Antonio8... at Yahoo! Answers Mark as irrelevant Undo

What is the cardinality of the set of all people who shall expel us from the paradise that Cantor has created?

Sweet descriptions of the empty set? In one of the mathematics classes I teach, we have been discussing cardinality (of both infinite and finite sets). So, on the assessment I'm giving them next week, there are some questions just asking "what is...

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The set of all seven letter words in this sentence.

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King Bee at Ask.Metafilter.Com Mark as irrelevant Undo

What is a data structure that, given a set of points and a query point, return all points in the set under a certain distance D away from the query point?

The problem is in 2-space and the metric of distance is Euclidean distance. (I want all points within a certain radius of a query point, which I think is different than something like k-nearest neighbors since we don't know k) Bonus points for a data...

Answer:

This problem is known as Fixed-radius near neighbors problem. The linked wikipedia article cites a very...

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Arun Iyer at Quora Mark as irrelevant Undo

The set t is defined to be all two digit multiples of 2 under 25. 1. How many subsets are there for t? 2. Create a set, v, that is a subset?

The Problem: The set T is defined to be all two digit multiples of 2 under 25. How many subsets are there for T? Create a set, V, that is a subset of T. State an element that is in T ...show more

Answer:

T = {10,12,14,16,18,20,22,24} There are 8 elements of the set. When calculating the number of subsets...

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FO3QPDWSOWTQYXIVK2HSTNOQNU at Yahoo! Answers Mark as irrelevant Undo

Answer:

Why not just use a permutation test?

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Justin Rising at Quora Mark as irrelevant Undo

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