What is closure: Definition and 169 Discussions

I've started to read a book called "Types and Programming Languages" and this excerpt is from the section entitled "Mathematical Preliminaries". Now I can justify the conclusion to myself by reflecting that there is no tuple in R' that is neither a member of R nor (s,s) with s a member of...

Given a finite set G is closed under an associative product and that both cancellation laws hold in G,Then G must be a group. I need to prove that G must be a group, I understand that for this I only need to show that : 1) There exist the identity 2) There exist the inverse. But...

Hello, I am currently working on proving the following theorem The boundary \partial A and the closure \overline{A} of a subset A of \mathbb C are closed sets. Proof: Let A \subset \mathbb C. We want to show the set \partial A \cap \overline{A} is closed. To show that \partial A...

What is "notion of closure" May I know what is "notion of closure", I don't need comprehensive explanation, I just want to understand what is meant by a set is closed under another set in order to proceed. For example, Set B is closed under Set A, does it mean that Set A is a strict...

Define: \mathbb{C}((t)) = \{t^{-n_0}\sum_{i=0}^{\infty}a_it^i\ :\ n_0 \in \mathbb{N}, a_i \in \mathbb{C}\} What is its algebraic closure? My notes say that it is "close" to: \bigcup _{m \in \mathbb{N}}\mathbb{C}((t))(t^{1/m}) where \mathbb{C}((t))(t^{1/m}) is the extention of the...

Peter Woit called attention to the liklihood that new WMAP data will be coming out soon for some additional detail here is a post from Anthony Lewis (Cambridge) http://cosmocoffee.info/viewtopic.php?p=1391#1391He says that around 23 March there will be one or more conference talks about the...

Hi. Can somebody please check my work!? I'm just not sure about 2 things, and if they are wrong, all my work is wrong. 1. Find a counter example for "If S is closed, then cl (int S) = S I chose S = {2}. I am not sure if S = {2} is an closed set? I think it is becasue S ={2} does not have an...

How do you do this proof? Isn't it already obvious given the definition? I have no idea how to go about writing it down. :confused: If someone could help me with this, I would really appreciate it. Thanks :) Sorry I had to write it in such a messy way. Define the closure of A as A closure =...

I have already got help with figuring this out. But i seem to be getting something wrong so maybe someone can check this over and tell me what I am doing wrong Q) find the angular momentum of a cone with heigh H and radius R now i was helped and told Rc = int (x)dv / int dV...

What is a "closure type"? I first encountered it by looking at the source of the uBLAS package from boost.org -- it's essentially an implementation of the BLAS using expression templates. I noticed that a lot of the classes have a nested typedef called "closure_type" (and a...

I wrote my code and try to setup the program , desperately the program closes it so quickly return 0 or getch() commands doesn't work how can I prevent it with a code ?

Let T be an element of B[0,1] be the set V=[B[0,1];f(1)=2]. Prove that T is closed (in metric space B[0,1]). I am not sure if it is obvious since I am new to this stuff but B[0,1] is an open ball I believe. My question is how do I find the complement of V. If I could define B/T then I am...

In his opening post on Chapter Seven of Gregg Rosenberg's A Place for Consciousness, Hypnagogue says this: Now there have already been several replies to this on the original thread, and most of them seem delighted that the unwarranted claim of physicalism that nature is causally closed...

If A \subset X where X has a topology, is it generally true that the interior of A is equal to the interior of the closure of A? This seems very reasonable to me, but probably only because I'm visualizing A as a disc in the real plane. If it isn't true, what would be a counterexample? thanks

I'm not studying algebra yet, I just happened to notice this and am curious. Mathworld's entry for the field axioms doesn't include closure axioms, but I have seen other authors include closure axioms in the field axioms. Does anyone know why this is or what difference it makes? Can closure be...

1) In R3 closure of an open ball is a closed ball, but this may not hold in general metric spaces. Can somebody give an example explaining the above statement? 2) what is a separable space? some good references are welcome. thanks for your help in advance. aditya...

If A is a bounded subset of the reals, show that the points infA, supA belong to the closure A*. At first the answer seems obvious to me since A* contains its limit points. I'm just having trouble putting it into words, any suggestions would be great, thanks.

Hi everyone, I need some closure on this problem: An engineer is designing a spring to be palced at the bottom of an elevator shaft. If the elevator cable should happen to break when the elevator is at a height h above the top of the spring, calculate the value of the spring constant k so...

EDIT: forgot to say, this is in response to another thread which had wandered way off its original question. Arguably this could be in at least 3 other forums end EDIT EDIT contains some gross errors, will correct them some timeEDIT OK, just wrote a long thread on this only to hit ctrl w...