Subsets Definition and 221 Threads

Homework Statement X=R real numbers, U in T, the topology <=> U is a subset of R and for each s in U there is a t>s such that [s,t) is a subset of U where [s,t) = {x in R; s<=x<t} Find the closure of each of the subsets of X: (a,b), [a,b), (a,b], [a,b] The Attempt at a Solution I don't...

* If p1,p2,……pm span Pn, write down a mathematical relationship between m and n. I know that Pn means the space of all polynomials of degree at most n, and this is an (n+1) dimension space, but I am not sure what kind of mathematical relationship the question is looking for :s Any help is...

I am having some troubles understanding the following, any help to me will be greatly appreciated. 1) Let S1 = {x E R^n | f(x)>0 or =0} Let S2 = {x E R^n | f(x)=0} Both sets S1 and S2 are "closed" >>>>>I understand why S1 is closed, but I don't get why S2 is closed, can anyone...

Homework Statement Show that if f: S -> Rn is uniformly continuous and S is bounded, then f(S) is bounded. Homework Equations Uniformly continuous on S: for every e>0 there exists d>0 s.t. for every x,y in S, |x-y| < d implies |f(x) - f(y)| < e bounded: a set S in Rn is bounded if it is...

Permutations of subsets with like objects Question Hello, I'd like to know if I solved the question correctly; if not, I'd appreciate some help. Question: Calculate the number of permutations for a subset of 3 objects from a superset of 8 objects where 5 are alike. My solution attempt...

Homework Statement Let: \alpha \in C_{4}[x] (the space of all 4-deg complex ploymonials) We'll define: U = Sp( \{\ x^3 - 2i \alpha x, x^2 +1 \} ) \\ W = Sp( \{\ x^3 + ix, (1-i)x^2 - \alpha x \}) as subspaces of C_{4}[x] a) find all values of alpha so that: W \cap U \neq \{ 0 \}...

How can I prove that \left| {\left\{ {A \subset \mathbb{N}:\left| A \right| \in \mathbb{N}} \right\}} \right| = \left| \mathbb{N} \right| ?

Hello everyone I'm confused on how he got this... the question says: Let S = {a,b,c} and for each integer i = 0, 1, 2, 3, let S_i be the set of all subests of S that have i elements. List the elements in S_o,S_1,S_2,S_3. Is {S_0,S_1,S_2,S_3} a partion of P(S)? Here is the answer...

Hello everyone. There arn't any problems like this in this section, so I'm kind of lost on what they want. It says... Let S = {a,b,c} and for each integer i = 0, 1, 2, 3 let S_i be the set of all subsets of S that have i elements. List the elemnts in S_o,S_1,S_2,S_3. Is {S_0,S_1,S_2,S_3}...

Hi all, Maybe i shud put it this way. Suppose I want to perform training on part of the data and leave the rest for testing. the training set is separated into subsets whereby I train one subset first, and use its weights and biases as weights to the next subset and so on. Then how to I write...

Hi all, Maybe i shud put it this way. Suppose I want to perform training on part of the data and leave the rest for testing. the training set is separated into subsets whereby I train one subset first, and use its weights and biases as weights to the next subset and so on. Then how to I write...

Can someone confirm/disprove the following: If X\subset\mathbb{P} is infinite, then \sum_{n\in X}\frac{1}{n} diverges or is irrational.

Suppose f:A--->B and S and T are subsets of A. Prove or give a counter example. (a) if S\subseteqT, then f(S)\subseteqf(T) (b) if f(S)\subseteqf(T), then S\subseteqT I know for a fact that (a) is true. The reason I say this is because if S\subseteqT ... then for example: Let S be the...

I have been reviewing my set theory and topology and recently came across an assertion I was not familiar with, and frankly have trouble grasping. In words, let I be a set (which is to serve as the set of indices), then for each \alpha \in I let A_\alpha be a subset of some set S. Now...

I'm just an interested laymn, and I'm trying to improve my knowledge in some areas where I'm weak. To this end, I found that Shilov's Elementary Real and Complex Analysis was highly recommended, and the Dover edition was available for only ten bucks, so how could I go wrong? But it didn't take...

Hi, I am having trouble with these proofs; I don't know if I am doing these right. I'd appreciate some help. Thank you. If X---> y is a map, then let B1, B2, B \subseteq X. i. f(B1 U B2) = f(B1) U f(B2) To prove this I have: f(B1 U B2)=f(B1) U f(B2) Since B1 U B2 \subseteq B1, we...

Having some difficult with general concepts of metric spaces: 1) What is the difference between a subset and a subspace. let's say we have metric space X. and A is a set in that space. Is A necessarily a metric space itself? 2) Why is the metric of X ( d(x,y) for x,y belonging to X )...

1. If a school offers 3200 separate courses and a survey of these courses determines that the class size is 50 with a standard deviation of 2, what would one expect for the average and standard deviation of a subset of 50 of these classes selected randomly? 2. In a survey to estimate the...

By definition, an infinite set is a set whose subset is proportional to the set which contains it. The sequence of numbers whether it be expressed as (n+1) or not, is infinite. Then (I am veturing into grounds I know little of here...) I am guessing it is safe to say that the numbers (n+1< or...

Show that the subsets of the plane are open: 1.) A= {(x,y)|-1<x<1,-1<y<1} 2.) C= {(x,y)|2<x2 + y 2<4} I have no clue on how to start with this problem. I have another question. What does this notation imply. f(x,y)=some function.

Hello, I am supposed to show that the number of proper subsets of S = {a1, a2, ... an} is 2^n - 1. I know that the number of subsets of S is 2^n. And I know also know that the number of proper subsets of S is 2^n - 1 since S is not a proper subset of itself. But how do I show that? I...