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Assuming a function Prime(x) that ordinally generates every prime for {x|x>0,x∈ℤ} and generates the primes in polynomial time, what would the efficiency (in layman's terms) be of an algorithm that:
-- Melab±1 ☎ 04:48, 12 August 2010 (UTC)
Hi, I'm trying to understand the notion of countable tightness ( http://en.wikipedia.org/wiki/Countable_tightness). So I have tried to find a simple example for a space which is not countably tight and came with te following example: Let X be the space of functions from R to {0,1}. Take the set A to be the set of all functions such that f(x) = 1 for a counable (which includes finite) set of x's and 0 otherwise. Then X is not a space of countable tightness since A is not closed in X but the intersection of A with any countable set of functions U is closed in U. Is this example OK? Also, I am trying to figure out, is the space of ultrafilters on R or on N for example is of countable tightness? Thanks! —Preceding unsigned comment added by Topologia clalit ( talk • contribs) 08:50, 12 August 2010 (UTC)
Forgot to mention, I am using the point open topology here... Topologia clalit ( talk) 08:54, 12 August 2010 (UTC)
Yes, but, isn't saying that accumulation points are limits of countable sequences, is the definition of a sequential space ( http://en.wikipedia.org/wiki/Sequential_space)? I mean, if we use your definition then what is the difference between a sequential space to a space with countable tightness? Topologia clalit ( talk) 11:01, 12 August 2010 (UTC)
Ok Thanks. So, these two are examples for non-countable tughtness spaces which helps me. Does anyone have an idea for a space which is of countable tightness but is not sequential? I'm still not sure I got the exact difference between these two definitions.. Thanks! Topologia clalit ( talk) 13:18, 12 August 2010 (UTC)
Thanks!!! Some of it is much clearer. But I think still miss some things here.. I mean, The Arens-Fort space is countable, then can't we make a sequense out of the whole space? Is the problem that our whole space sequence will "get in and out" an infinite number of times for any open neighborhood of (0,0)? I'm not quite sure I understand what does a column mean.. If our pairs is of the form (n,m), then, a column means something like all the pairs of the form (n,5) for example? Topologia clalit ( talk) 15:12, 12 August 2010 (UTC)
Got it. Thanks! Topologia clalit ( talk) 06:21, 13 August 2010 (UTC)
According to Pearson product-moment correlation coefficient, the formula is:
However, according to the following University
website, the formula is:
How can this be? -
114.76.235.170 (
talk) 12:23, 12 August 2010 (UTC)
I think we have a problem here. The definition above uses r, but that's meant to be used for the sample correlation coefficient! That formula above is for the population correlation coefficient. Shouldn't this be using ρ, instead of r? - 114.76.235.170 ( talk) 14:41, 12 August 2010 (UTC)
In fact, my textbook says that it is:
What am I missing? - 114.76.235.170 ( talk) 14:54, 12 August 2010 (UTC)
Someone's not being entirely careful about the sample-versus-population issue. I'd use the Greek letters for the population means, not for sample means. Michael Hardy ( talk) 17:04, 12 August 2010 (UTC)
Imagine a random quadrilateral (not parallelogram, not kite etc.). Prove that the sum of 3 sides is longer than the remaining side.-- Mikespedia is on Wikipedia! 17:32, 12 August 2010 (UTC)
As "they" say, "A straight line is the shortest distance between two points." That "remaining side" is a straight line. So there. Michael Hardy ( talk) 23:34, 13 August 2010 (UTC)
Could someone explain the proof in less-advanced terms? I'm not a TCS expert and the Wikipedia article only has two sentences about the proof. -- 70.134.48.188 ( talk) 19:29, 12 August 2010 (UTC)
Ok, so a couple of us are studying for an upcoming analysis test and came upon a question which we couldn't answer so we appeal to higher authorities here. The question asks for an example of a Hilbert space H and a sequence of operators on H such that
i) for all n=1,2,3,...
ii) the operators converge strongly as
iii) The strong limit of the operators is not compact.
Any help/hints would be greatly appreciated. Thanks!
174.29.63.159 (
talk) 19:54, 12 August 2010 (UTC)
Wow, I don't think I have ever felt dumber than this before.
174.29.63.159 (
talk) 01:39, 13 August 2010 (UTC)
Wait, sorry! The example you gave is perfect but I asked the wrong question. I wanted to ask for a sequence of COMPACT operators each with norm less than or equal to one such that their partial sums (properly scaled) converge strongly to something not compact. Thanks! 174.29.63.159 ( talk) 04:53, 13 August 2010 (UTC)
What is the topology of the "space" of p-planes through the origin in n-space?
This question is motivated by the problem of choosing a basis for orthographic projection from n-space into 2– or 3-space; I want to avoid some parts of the solution-space, and to do that I need to know what the solution-space is! — Tamfang ( talk) 21:46, 12 August 2010 (UTC)
Mathematics desk | ||
---|---|---|
< August 11 | << Jul | August | Sep >> | August 13 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Assuming a function Prime(x) that ordinally generates every prime for {x|x>0,x∈ℤ} and generates the primes in polynomial time, what would the efficiency (in layman's terms) be of an algorithm that:
-- Melab±1 ☎ 04:48, 12 August 2010 (UTC)
Hi, I'm trying to understand the notion of countable tightness ( http://en.wikipedia.org/wiki/Countable_tightness). So I have tried to find a simple example for a space which is not countably tight and came with te following example: Let X be the space of functions from R to {0,1}. Take the set A to be the set of all functions such that f(x) = 1 for a counable (which includes finite) set of x's and 0 otherwise. Then X is not a space of countable tightness since A is not closed in X but the intersection of A with any countable set of functions U is closed in U. Is this example OK? Also, I am trying to figure out, is the space of ultrafilters on R or on N for example is of countable tightness? Thanks! —Preceding unsigned comment added by Topologia clalit ( talk • contribs) 08:50, 12 August 2010 (UTC)
Forgot to mention, I am using the point open topology here... Topologia clalit ( talk) 08:54, 12 August 2010 (UTC)
Yes, but, isn't saying that accumulation points are limits of countable sequences, is the definition of a sequential space ( http://en.wikipedia.org/wiki/Sequential_space)? I mean, if we use your definition then what is the difference between a sequential space to a space with countable tightness? Topologia clalit ( talk) 11:01, 12 August 2010 (UTC)
Ok Thanks. So, these two are examples for non-countable tughtness spaces which helps me. Does anyone have an idea for a space which is of countable tightness but is not sequential? I'm still not sure I got the exact difference between these two definitions.. Thanks! Topologia clalit ( talk) 13:18, 12 August 2010 (UTC)
Thanks!!! Some of it is much clearer. But I think still miss some things here.. I mean, The Arens-Fort space is countable, then can't we make a sequense out of the whole space? Is the problem that our whole space sequence will "get in and out" an infinite number of times for any open neighborhood of (0,0)? I'm not quite sure I understand what does a column mean.. If our pairs is of the form (n,m), then, a column means something like all the pairs of the form (n,5) for example? Topologia clalit ( talk) 15:12, 12 August 2010 (UTC)
Got it. Thanks! Topologia clalit ( talk) 06:21, 13 August 2010 (UTC)
According to Pearson product-moment correlation coefficient, the formula is:
However, according to the following University
website, the formula is:
How can this be? -
114.76.235.170 (
talk) 12:23, 12 August 2010 (UTC)
I think we have a problem here. The definition above uses r, but that's meant to be used for the sample correlation coefficient! That formula above is for the population correlation coefficient. Shouldn't this be using ρ, instead of r? - 114.76.235.170 ( talk) 14:41, 12 August 2010 (UTC)
In fact, my textbook says that it is:
What am I missing? - 114.76.235.170 ( talk) 14:54, 12 August 2010 (UTC)
Someone's not being entirely careful about the sample-versus-population issue. I'd use the Greek letters for the population means, not for sample means. Michael Hardy ( talk) 17:04, 12 August 2010 (UTC)
Imagine a random quadrilateral (not parallelogram, not kite etc.). Prove that the sum of 3 sides is longer than the remaining side.-- Mikespedia is on Wikipedia! 17:32, 12 August 2010 (UTC)
As "they" say, "A straight line is the shortest distance between two points." That "remaining side" is a straight line. So there. Michael Hardy ( talk) 23:34, 13 August 2010 (UTC)
Could someone explain the proof in less-advanced terms? I'm not a TCS expert and the Wikipedia article only has two sentences about the proof. -- 70.134.48.188 ( talk) 19:29, 12 August 2010 (UTC)
Ok, so a couple of us are studying for an upcoming analysis test and came upon a question which we couldn't answer so we appeal to higher authorities here. The question asks for an example of a Hilbert space H and a sequence of operators on H such that
i) for all n=1,2,3,...
ii) the operators converge strongly as
iii) The strong limit of the operators is not compact.
Any help/hints would be greatly appreciated. Thanks!
174.29.63.159 (
talk) 19:54, 12 August 2010 (UTC)
Wow, I don't think I have ever felt dumber than this before.
174.29.63.159 (
talk) 01:39, 13 August 2010 (UTC)
Wait, sorry! The example you gave is perfect but I asked the wrong question. I wanted to ask for a sequence of COMPACT operators each with norm less than or equal to one such that their partial sums (properly scaled) converge strongly to something not compact. Thanks! 174.29.63.159 ( talk) 04:53, 13 August 2010 (UTC)
What is the topology of the "space" of p-planes through the origin in n-space?
This question is motivated by the problem of choosing a basis for orthographic projection from n-space into 2– or 3-space; I want to avoid some parts of the solution-space, and to do that I need to know what the solution-space is! — Tamfang ( talk) 21:46, 12 August 2010 (UTC)