- Jan 2024
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Local file Local file
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Mordell’s theorem,which says that the group of rational points on an elliptic curve is finitelygenerated;
Mordell's theorem indicates that the group of rational points on an elliptic curve is finitely generated.
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a special case of Hasse’s theorem, due to Gauss, which de-scribes the number of points on an elliptic curve defined over a finite field.
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Nagell–Lutz theorem, which gives a precise procedure for finding all of therational points of finite order on an elliptic curve;
The Nagell-Lutz theorem provides a constructive algorithm on elliptic curves for finding all of the ration points of finite order.
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- Dec 2023
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docdrop.org docdrop.org
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what you're referring to is the idea that people come together and through language culture and story they have narratives that then create their own realities like the 00:12:04 sociologist abely the sociologist wi Thomas said if people think people believe things to be real then they are real in their consequences
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for: Thomas Theorem, The definition of the situation, William Isaac Thomas, Dorothy Swain Thomas, definition - Thomas Theorem, definition - definition of the situation, conflicting belief systems - Thomas theorem, learned something new - Thomas theorem
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definition: Thomas Theorem
- definition: definition of the situation
- "The Thomas theorem is a theory of sociology which was formulated in 1928 by William Isaac Thomas and Dorothy Swaine Thomas:
If men define situations as real, they are real in their consequences.[1]
In other words, the interpretation of a situation causes the action. This interpretation is not objective. Actions are affected by subjective perceptions of situations. Whether there even is an objectively correct interpretation is not important for the purposes of helping guide individuals' behavior.|
- comment
- learned something new
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key insight: polarization
- Behaviors subsequently are enacted out of a set of beliefs.
- If there are a multitude of conflicting belief systems emerged from different cultures, then real conflicts can emerge out of the disharmony of conflicting beliefs
- This is a very important insight into the polarization we see in the world today
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adjacency between:
- polarization
- Thomas Theorem
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adjacency statement
- polarization can be explained by the Thomas Theorem
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reference
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- Oct 2023
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www.reddit.com www.reddit.com
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What is it with index cards ? .t3_17ck5la._2FCtq-QzlfuN-SwVMUZMM3 { --postTitle-VisitedLinkColor: #9b9b9b; --postTitleLink-VisitedLinkColor: #9b9b9b; --postBodyLink-VisitedLinkColor: #989898; } So I posted a while ago about my journey into the zettlekasten and I have to admit I still enjoy using this system for notes.I must say, I am an avid note taker for a long time. I write ideas, notes from books, novels, poems and so much more. I mainly used to use notebooks, struggle a while with note taking apps and now I mainly use two kind of things : index cards (A6) and an e-ink tablet (the supernote) for different purpose of course, the index cards for the zettelkasten and the e-ink tablet for organization and my work. To be honest I used to consider myself more a notebooks kind of person than an index cards one (and I am from France we don't use index cards but "fiche bristol" which are bigger than A6 notecards, closer to an A5 format)Still, there is something about index cards, I cannot tell what it is, but it feels something else to write on this, like my mind is at ease and I could write about ideas, life and so many stuff covering dozens of cards. I realize that after not touching my zettelkasten for a few week (lack of time) and coming back to it. It feels so much easier to write on notecards than on notebooks (or any other place) and I can't explain it.Anyone feeling the same thing ?
reply to u/Sensitive-Binding at https://www.reddit.com/r/antinet/comments/17ck5la/what_is_it_with_index_cards/
Some of it may involve the difference in available space versus other forms of writing on larger pages of paper. Similarly, many find that there is less pressure to write something short on Twitter or similar social media platforms because there is less space in the user interface that your mind feels the need to fill up. One can become paralyzed by looking at the larger open space on a platform like WordPress with the need to feel like they should write more.
With index cards you fill one up easily enough, and if there's more, you just grab another card and repeat.
cross reference with Fermat's Last Theorem being easier to suggest in a margin than actually writing it out in full.
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- Aug 2023
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hub.jhu.edu hub.jhu.edu
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"But there's a very famous theorem in topology called the Jordan curve theorem. You have a plane and on it a simple curve that doesn't intersect and closes—in other words, a loop. There's an inside and an outside to the loop." As Riehl draws this, it seems obvious enough, but here's the problem: No matter how much your intuition tells you that there must be an inside and an outside, it's very hard to prove mathematically that this holds true for any loop that can be drawn.
How does one concretely define "inside" and "outside"? This definition is part of the missing space between the intuition and the mathematical proof.
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- May 2023
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8.3.1. I NTEGRAL C ONVERGENCE T HEOREM
Integral of the limit of uniform converging function is the same as the integral of the lmit. Pay attention to conditions: 1. Closed and bounded interval \([a, b]\). 2. Sequence of CONTINUOUS functions. 3. Of course, converges uniformly.
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Local file Local file
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4.7-3 Uniform Boundedness Theorem.
A sequence of linear operator such that, pointwise the value of the linear operators are bounded is enough for the norm of the operator to be bounded for the limit of the sequence of linear operators.
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4.4-1 Riesz's Theorem (Functionals on C[a, b]).
Every Bounded linear functionals on C[a, b] is Riemann Integrals.
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4.8-4 Theorem (Strong and weak convergence).
Strong convergence, equivalences and converse.
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4.3-3 Theorem (Bounded linear functionals).
Bounded Linear Functional Theorems in Banach Space.
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4.3-2 Hahn-Banach Theorem (Normed spaces).
Hahn Banach Theorem in normed vector spaces
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4.2-1 Hahn-Banach Theorem (Extension of linear functionals).
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- Apr 2023
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4.3.8. T HEOREM .
open set, closed complement and vice versa. In finite Euclidean space.
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www.dl.behinehyab.com www.dl.behinehyab.com
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Theorem 5.7.
Complexity of the Floyd warshall Algorithm.
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Theorem 11.9 (Triangularity Property).
the incidence matrix of a spanning tree graph can be, lower triangular.
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Theorem 11.2 (Spanning Tree Property).
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Theorem 11.1 (Cycle Free Property).
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Theorem 9.5 (Weak Duality Theorem)
(9.11) is literally the dual LP formulation of the min cost flow problem onthe network.
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Theorem 9.4 (Complementary Slackness Optimality Conditions)
Some flow is optimal, if and only if, there is some potential, where, the reduced costs for the potential satisfies the complementary slackness conditions for the duality of the linear program of the min cos flow problem.
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Local file Local file
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2.10-4 Theorem (Dual space).
The dual spaces theorem
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2.10-2 Theorem (Completeness)
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2.10-1 Theorem (Space B(X, Y».
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2.9-1 Theorem (Dimension of X*).
The space and the dual space is having the same dimension.
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2.8-3 Theorem (Continuity and boundedness)
It's an example of theorem 2.7-9. A linear operator has boundedness and continuity being an equivalent conditions.
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2.7-9 Theorem (Continuity and boundedness)
Let T be a linear mapping between 2 normed space, then:
- T is continous if and only if it's bounded.
- T is continous at a single point then it's continous.
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2.7-8 Theorem (Finite dimension).
Linear operator, and bounded linear operators are equivalent when the vector space is finite dimensional.
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2.6-9 Theorem (Range and null space).
- Range is a vector space.
- If the dim of the range is less than infinitely, then the dim of the range is \(\le\) dim of the domain.
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2.5-6 Theorem (Continuous mapping)
Continuous mapping preserves compactness in finite dimensional spaces.
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2.5-5 Theorem (Finite dimension)
Compact Closed unit ball in a normed spaces would mean that we have finite dimension.
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2.5-3 Theorem (Compactness).
compactness is euivalent to closed and boundedness in finite dimensional spaces.
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Local file Local file
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18.1 Theorem.
extreme value theorem. A continuous function attains some type of minimum and maximum over an compact set in its domain.
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11.4 Theorem.
Monotone Subsequence Theorem for real Sequences.
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homepages.uc.edu homepages.uc.edu
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heorem 6.5 (Sufficient Conditions for Differentiability).
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Theorem 6.4.
A Necessary conditions for a function to he differentiable at a point.
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Local file Local file
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1.9 Theorem (attainment of a minimum)
The existence of a minimizer for functions.
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- Mar 2023
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Local file Local file
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2.4-5 Theorem (Equivalent norms).
In a finite dimensional space, every norm is Equivalent
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2.4-3 Theorem (Closedness)
Every finite dimensional Banach space is closed.
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2.4-2 Theorem (Completeness).
Every finite dimension subspace of the normed space is complete, so are their subspace.
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2.3-2 Theorem (Completion)
Alternative explanations from Walfram Math world: here.
In brief, you can use an isometry map from a banach space to another subspace in a different Banach space such that it's dense.
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2.3-1 Theorem (Subspace of a Banach space).
Similar to 1.4-7
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www.dl.behinehyab.com www.dl.behinehyab.com
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Theorem 9.7.
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Theorem 9.6 (Strong Duality Theorem)
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Theorem 9.3 (Reduced Cost Optimality Conditions)
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Theorem 9.1
no negative cycles optimal solutions min cost flow theorem
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Theorem 9.10
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Theorem 7.10
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Theorem 5.3
The complexity of the FIFO label correcting algorithms.
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Theorem 7.4
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Theorem 3.5 (Flow Decomposition Theorem).
We implicitly assume that the flow is positive due to how the algorithm works.
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Theorem 6.12.
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Theorem 6.10 (Generalized Max-Flow Min-Cut Theorem).
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localhost:4000 localhost:4000
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THEOREM 23.8
Subgradient sum rules
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THEOREM 23.7.
Normal cone of the non smooth level plot of a function.
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- Feb 2023
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www.dl.behinehyab.com www.dl.behinehyab.com
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Theorem 6.6.
complexity of the max flow labeling algorithm.
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Theorem 6.7.
Min cut capacity and the cardinality of maximum number of arc disjoint path from source to destination.
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Theorem 6.3 (Max-Flow Min-Cut Theorem).
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Theorem 6.4 (Augmenting Path Theorem).
Aug Path theorem
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Theorem 6.5 (Integrality Theorem).
Network flow integers theorem.
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Theorem 6.8
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Theorem 5.1 (Shortest Path Optimality Conditions).
There is a linear programming interpretation via the network flow standard form and the reduction of shortest path to the network flow problem at the end of chapter 5.2.
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Theorem 3.7 (Augmenting Cycle Theorem).
Given 2 feasible flow, \(x, x^\circ\), it's possible to construct \(x\) with at most m directed cycles on the residual graph \(G(x^\circ)\).
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Theorem 3.8 (Negative Cycle Optimality Theorem).
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Local file Local file
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5.1-4 Theorem (Contraction on a ball)
Paculiar, I have no idea about the significant of this theorem and why it's stated here. How does this variation of the theorem even make inuitive sense?
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5.1-2 Banach Fixed Point Theorem
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1.4-7 Theorem (Complete subspace)
theorem
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1.4-6 Theorem (Closure, closed set).
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Local file Local fileBOOK1
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Theorem 3.2.5
Characterization of a limit point of a set via a limit that occurs inside of the set.
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royalsocietypublishing.org royalsocietypublishing.org
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Bell’s theorem is aboutcorrelations (joint probabilities) of stochastic real variables and therefore doesnot apply to quantum theory, which neither describes stochastic motion nor usesreal-valued observables
strong statement, what do people think about this? is it accepted by anyone or dismissed?
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Theorem 29
Theorem:
metric equivalences preserves sequential convergence and openedness of sets.
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Theorem 24
A convergence sequence is a Cauchy sequence under a certain metric.
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Theorem 27
sequential continuity of a mapping in the metric space.
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Theorem 13
For an accumulation point in a subset \(M\) of space \(X\), any epsilon balls with central isolation has ifninitely many points and there is a sequence in such epsilon ball such that it converges to the singularity but never really being on the singularity.
Singularity: \(x_0\) as described in the proof.
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Theorem 25
The equivalence of the sequential closedness of a set and the epsilon ball closedness of a set.
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- Nov 2022
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en.wikipedia.org en.wikipedia.org
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it became clear that Fermat's Last Theorem could be proven as a corollary of a limited form of the modularity theorem (unproven at the time and then known as the "Taniyama–Shimura–Weil conjecture"). The modularity theorem involved elliptic curves, which was also Wiles's own specialist area.[15][16]
Elliptical curves are also use in Ed25519 which are purportedly more robust to side channel attacks. Could there been some useful insight from Wiles and the modularity theorem?
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- Jan 2022
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towardsdatascience.com towardsdatascience.com
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Central Limit Theorem
the Central Limit Theorem tells us the sampling distribution of X̄ is closely approximated to a normal distribution.
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- May 2021
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twitter.com twitter.com
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🔥 Kareem Carr 🔥 on Twitter. (n.d.). Twitter. Retrieved 1 May 2021, from https://twitter.com/kareem_carr/status/1383925269132582912
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- Jun 2019
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mitpressonpubpub.mitpress.mit.edu mitpressonpubpub.mitpress.mit.edu
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Or do you recall jotting down formulae for molecules and compounds in the margins of your chemistry textbook?
I can't help but think of one of the biggest and longest standing puzzles in mathematics in Fermat's Last Theorem. He famously wrote in the margin of a book that he had a proof. but that it was too large to fit in the margin.
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- Jun 2017