Mark all statements that are true (there might be more than one statement that is true). If A CR is countably infinite then A is not compact. Let {x} be a real sequence and A={x: n€ N}, where x = R. Define A = {x: n> k}, keN and let B ={A : keN). Then B is a covering k of A that has a finite subcovering. O Let {x} be a real sequence and assume that x n Let B=(0, {co. 1 1: 1 EN}. 1 n n of A. O Let {x} be a real sequence and A={ →x. Then A= = {x₁ : nENU {x} is sequentially compact. n then B is not empty. = {x₁ : n=N}, where x E R. Define A = {x : n ≥ k}, k € N and let B = { n n = {A₁: k@N}. Then is a covering
Mark all statements that are true (there might be more than one statement that is true). If A CR is countably infinite then A is not compact. Let {x} be a real sequence and A={x: n€ N}, where x = R. Define A = {x: n> k}, keN and let B ={A : keN). Then B is a covering k of A that has a finite subcovering. O Let {x} be a real sequence and assume that x n Let B=(0, {co. 1 1: 1 EN}. 1 n n of A. O Let {x} be a real sequence and A={ →x. Then A= = {x₁ : nENU {x} is sequentially compact. n then B is not empty. = {x₁ : n=N}, where x E R. Define A = {x : n ≥ k}, k € N and let B = { n n = {A₁: k@N}. Then is a covering
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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Transcribed Image Text:Mark all statements that are true (there might be more than one statement that is true).
If A CR is countably infinite then A is not compact.
Let {x} be a real sequence and A={x: n≤N}, where x € R. Define A = {x: n≥ k}, k € N and let B = {A : KEN). Then B is a covering
k
of A that has a finite subcovering.
O Let {x} be a real sequence and assume that x
n
0
Let
·{co. - 1
n
Let B=(0,
1: 1€N}. 1
n
→x. Then A= = {x₁: : nENU {x} is sequentially compact.
n
then B is not empty.
{x} be a real sequence and A={
= {x: n=N}, where x E R. Define A = {x : n ≥ k}, k € N and let B = {
n
n
of A.
Then is a covering
= {Ak: k=N}. *
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