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Office_Shredder's latest activity
O
Office_Shredder
replied to the thread
Proving convergence of sequence from convergent subsequences
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Proving the set of indices not in the subsequence converges is really roundabout. Given ##\epsilon>0## there exists ##n_k## such that...
Today, 7:06 AM
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Office_Shredder
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FactChecker's post
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Prove the identity matrix is unique
with
Like
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Sorry, I missed that. Ok. I see that is part of the goal of the question. Suppose that you show that the matrix ##I## =...
Yesterday, 5:36 PM
O
Office_Shredder
replied to the thread
Finding where a function is sign definite, sign indefinite or sign semidefinite
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What is the definition of sign definite/semi definite/indefinite?
Thursday, 5:35 AM
O
Office_Shredder
replied to the thread
A
Existence of a limit implies that a function can be harmonic extended
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It's an annoying quirk that you need double # instead of single $ to make in line latex, if you could edit your post to find and replace...
May 29, 2024
O
Office_Shredder
replied to the thread
POTW
Find the Dimension of a Subspace of Matrices
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I've always felt like it's a flaw of linear algebra that more matrices don't commute with diagonal matrices
May 27, 2024
O
Office_Shredder
replied to the thread
A
Can three elbows generate any point in space?
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I think you only need one turn? Assuming your arms can have arbitrary length, the first arm can reach the (x,y,0) point corresponding to...
May 27, 2024
O
Office_Shredder
replied to the thread
Ratio test proof
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A good starting point is to compare it to a geometric series. For example if ##c=1/3## can you think of a series that converges whose...
May 27, 2024
O
Office_Shredder
replied to the thread
Find f s. t. ||f||=1 and f(x) < 1 with ||x||=1
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Suppose ##f## is continuous and ##f(A)=B##, where ##A## is compact. Let ##U_i## be an open infinite cover of ##B## and consider...
May 26, 2024
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Office_Shredder
replied to the thread
I
Question about vector spaces and subsets
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I'm going to do things over two dimensions, to make the difference between scalars and vectors a bit more obvious. ##\mathbb{Q}^2## is...
May 26, 2024
O
Office_Shredder
replied to the thread
Find f s. t. ||f||=1 and f(x) < 1 with ||x||=1
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No, for example the sequence ##x_k=(1,0)## when ##k## is odd and ##(0,1)## when ##k## is even does not converge. But it is true that...
May 25, 2024
O
Office_Shredder
replied to the thread
Find f s. t. ||f||=1 and f(x) < 1 with ||x||=1
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Item 1 does not exist. The key point is for the supremum to be 1 but the maximum to be less than 1, there must exist a sequence ##x_n##...
May 25, 2024
O
Office_Shredder
replied to the thread
I
Question about vector spaces and subsets
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Counterpoint: ##\mathbb{Q}\subset \mathbb{R}##, is a 1 dimensional vector space over itself but it's not a subspace of the one...
May 22, 2024
O
Office_Shredder
replied to the thread
I
How to implement proper error estimation using MC
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You can kind of just compute this exactly. For any possible choice of x, you know what fraction of the time your sampling will return a...
May 22, 2024
O
Office_Shredder
replied to the thread
I
How to implement proper error estimation using MC
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Are y and the standard deviation of dy exactly known to you?
May 22, 2024
O
Office_Shredder
replied to the thread
I
A step in a proof of linear dependence of ODE solutions
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I think the point is that for any fixed x the functions are just numbers.
May 21, 2024
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