# User contributions

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- 20:00, 15 July 2019
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**(+1,651)** . . N Shattering (Created page with "Let <math>\mathcal H</math> be a class of functions from <math>\mathcal X</math> to <math>\{0,1\}</math>, called a hypothesis class. Let <math>S = \{p_1, \ldots, p_n\} \subset...") - 20:28, 12 July 2019
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**(+651)** . . N User:IssaRice/Computability and logic/Rogers fixed point theorem using Sipser's notation (Created page with "Sipser's textbook presents the recursion theorem, but not the fixed point theorem. Here is one way to state the fixed point theorem using Sipser's notation. '''Theorem''' (Fi...") - 07:24, 6 July 2019
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**(+864)** . . N User:IssaRice/Isometry in metric spaces (Created page with "when playing around with metric spaces, one might notice that certain metric spaces can be "modeled" by other metric spaces. For instance, let <math>X = \{1,2,3\}</math> be a...") - 07:09, 6 July 2019 (diff | hist) . . (+438) . . N User:IssaRice/Construction of the real numbers (Created page with "something that i have seen clarified ''exactly once'' is why constructing the real numbers (for instance via dedekind cuts or equivalence classes of cauchy sequences of ration...")
- 04:24, 6 July 2019
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**(+1,143)** . . N User:IssaRice/Adherent point and limit point (Created page with "Let <math>(X,d)</math> be a metric space, let <math>E</math> be a subset of <math>X</math>, and let <math>x_0\in X</math> be a point. * there exists a sequence <math>(x_n)_{n...") - 03:42, 5 July 2019 (diff | hist) . . (+210) . . N User:IssaRice/Subfield of math that is best for introducing proofs (Created page with "==Real analysis== Pros: Cons: ==Linear algebra== Pros: Cons: ==Abstract algebra== Pros: Cons: ==Computability and logic== Pros: Cons: ==Discrete math== Pros: Con...")
- 21:50, 27 June 2019
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**(+531)** . . N User:IssaRice/Linear algebra/Linear transformation vs matrix views (Created page with "Given an <math>m\times n</math> matrix <math>A</math> we can define a linear map <math>T : \mathbf R^n \to \mathbf R^m</math> by <math>T(x) = Ax</math>. Given a linear map <m...") - 00:46, 25 June 2019 (diff | hist) . . (+1) . . N User:IssaRice/Logical inductor construction (Created page with ".")
- 00:09, 19 June 2019
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**(+1,230)** . . N User:IssaRice/Computability and logic/Sipser's quine in Python (Created page with "Michael Sipser's ''Introduction to the Theory of Computation'' describes a quine using Turing machines. Here is an implementation of the machine ''SELF''. <pre>TAPE = "" de...") - 05:38, 10 June 2019
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**(+2,281)** . . N User:IssaRice/Subsets of the reals that can define their own convergence (Created page with "(probably not very important) Something that has bugged me about the Cauchy sequence construction of the reals is that in the definition of Cauchyness/convergence, a rational...") - 02:34, 7 June 2019 (diff | hist) . . (+440) . . N User:IssaRice/Linear algebra/Rank (Created page with "<math>T : V \to W</math> <math>A</math> is m by n matrix * <math>\dim \operatorname{range} T</math> * dimension of row space of <math>A</math> * dimension of column space of...")
- 22:18, 1 June 2019
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**(+2,063)** . . N User:IssaRice/Extreme value theorem (Created page with "Working through the proof in Pugh's book by filling in the parts he doesn't talk about. Let <math>M = \sup\{f(x) : x \in [a,b]\}</math> and <math>X = \{x \in [a,b] : \sup V_x...") - 08:02, 25 April 2019 (diff | hist) . . (+131) . . N User:IssaRice/Computability and logic/List of important distinctions in mathematical logic (IssaRice moved page User:IssaRice/Computability and logic/List of important distinctions in mathematical logic to User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic) (current)
- 18:03, 17 April 2019
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**(+2,052)** . . N Abstracting sensory data in Solomonoff induction (Created page with "One potential misconception one might have about Solomonoff induction is the degree to which one "abstracts" the sensory information that Solomonoff induction is "allowed...") - 16:56, 17 April 2019
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**(+662)** . . N Proportion of valid programs view of Solomonoff induction (Created page with "'''Proportion of valid programs view of Solomonoff induction''' is one of several ways of viewing the deterministic variant of Solomonoff induction. This view roughly says...") - 00:12, 16 April 2019
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**(+1,252)** . . N Equivalence of random coinflips view and minimal programs view (Created page with "Two of the several ways of viewing the deterministic variant of Solomonoff induction are: * The "random coinflips view": Given a monotone Turing machine, we feed the machine...") - 02:26, 31 March 2019 (diff | hist) . . (+60) . . N Variants of Solomonoff induction (Created page with "This page lists some '''variants of Solomonoff induction'''.")
- 20:25, 25 March 2019 (diff | hist) . . (+118) . . N User:IssaRice/Computability and logic/Computability of the uncountable (Created page with "* http://jdh.hamkins.org/alan-turing-on-computable-numbers/ * stillwell's reverse mathematics, p. 77 * Hay 2007, p. 31")
- 22:08, 24 March 2019 (diff | hist) . . (+422) . . N User:IssaRice/Computability and logic/Bounded computation trick (Created page with "Instead of saying "compute this thing" you can say "compute this thing for <math>n</math> steps", then let <math>n</math> vary. This trick makes the computation bounded, which...")
- 19:51, 21 March 2019 (diff | hist) . . (+493) . . N Solomonoff induction (Created page with "'''Solomonoff induction''' is an idealized method of sequence prediction. ==Variants== There are many variants of Solomonoff induction that seem to all turn out essentially...")
- 19:35, 20 February 2019
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**(+695)** . . N User:IssaRice/Computability and logic/List of possibilities for completeness and decidability (Created page with "{| class="sortable wikitable" |- ! Decidable logic? !! Complete logic? (semantic completeness) !! Decidable theory? !! Complete theory? (negation-completeness) !! Example or p...") - 07:21, 17 February 2019 (diff | hist) . . (+43) . . N Hunting for Simpson's paradox (IssaRice moved page Hunting for Simpson's paradox to Recognizing Simpson's paradox) (current)
- 22:37, 10 February 2019
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**(+617)** . . N User:IssaRice/Computability and logic/Some important distinctions and equivalences in introductory mathematical logic (Created page with "This page lists some important distinctions in introductory mathematical logic. * completeness: semantically complete (complete logic; the topic of the completeness theorem)...") - 02:56, 10 February 2019 (diff | hist) . . (+228) . . N User:IssaRice/Computability and logic/Eliezer Yudkowsky's Löb's theorem puzzle (Created page with "original link: https://web.archive.org/web/20160319050228/http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/ current LW link: https://www.lesswrong.com/posts/...")
- 20:56, 9 February 2019 (diff | hist) . . (+299) . . N User:IssaRice/Computability and logic/Logic versus theory (Created page with "Many terms in mathematical logic apply to both logics and to theories. In these cases, the terms mean different things depending on what object it applies to. {| class="wikit...")
- 00:31, 9 February 2019 (diff | hist) . . (+214) . . N User:IssaRice/Computability and logic/Entscheidungsproblem (Created page with "'''Entscheidungsproblem''', also called '''Hilbert's decision problem''' is a problem in mathematical logic. ==Equivalent formulations== {| class="wikitable" |} ==See also=...")
- 02:03, 8 February 2019 (diff | hist) . . (+210) . . N User:IssaRice/Computability and logic/Diagonalization lemma (Created page with " ==Rogers's fixed point theorem== Let <math>f</math> be a total computable function. Then there exists an index <math>e</math> such that <math>\varphi_e \simeq \varphi_{f(e)}...")
- 01:04, 7 February 2019 (diff | hist) . . (+431) . . N User:IssaRice/Computability and logic/Expresses versus captures (Created page with "The ''expresses versus captures'' distinction is an important one in mathematical logic, but unfortunately the terminology differs wildly between different texts. The followin...")
- 08:53, 6 February 2019
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**(+792)** . . N User:IssaRice/Multiplicative process (Created page with " ==Notes== * https://www.greaterwrong.com/posts/8jwAvGtrwvKHYgoC7/the-tails-coming-apart-as-a-strategy-for-success especially [https://www.greaterwrong.com/posts/8jwAvGtrwvKH...") - 01:09, 1 February 2019 (diff | hist) . . (+374) . . N User:IssaRice/Computability and logic/Theory (Created page with "In mathematical logic, '''theory''' has several related meanings. * theory as set of sentences * theory as set of sentences closed under deduction * theory as something with...") (current)
- 21:46, 30 January 2019
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**(+1,059)** . . N User:IssaRice/Computability and logic/Intuitiveness and simplicity tradeoff (Created page with "In various places in computability and logic, there is a tradeoff between the intuitiveness of a formalization and its inherent simplicity. Some examples: * The more our ded...") (current) - 03:39, 23 January 2019
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**(+1,217)** . . N User:IssaRice/Computability and logic/Comparison of intuitive notions of computability and proof (Created page with "See Boolos/Burgess/Jeffrey, p. 185. {| class="sortable wikitable" ! !! Computability !! Mathematical proof |- | Intuitive notion || effectively computable/effectively calcula...") - 03:48, 16 January 2019 (diff | hist) . . (+447) . . N Variance (Created page with "The variance of a random variable <math>X</math> is defined as <math>\mathrm{Var}(X) := \mathbf E[(X - \mathbf EX)^2]</math>, where <math>\mathbf EX</math> is the expectatio...")
- 03:15, 16 January 2019 (diff | hist) . . (+25) . . N Expected value (Redirected page to Expectation) (current)
- 03:04, 16 January 2019 (diff | hist) . . (+12) . . N Expectation (Created page with "==Notation==")
- 05:51, 15 January 2019 (diff | hist) . . (+41) . . N Category:Probability (Created page with "Pages about topics in probability theory.") (current)
- 05:39, 15 January 2019 (diff | hist) . . (+384) . . N Disappearance of sample space (Created page with "In probability theory, the "orthodox approach" defines events, probability measure, random variable, etc., in terms of a sample space (often denoted <math>\Omega</math>). Howe...")
- 02:51, 15 January 2019 (diff | hist) . . (+258) . . N List of sample space perspectives (Created page with "In probability theory, one can take several perspectives of what the sample space (often denoted <math>\Omega</math>) means. We record several of these here. * Possible world...")
- 00:35, 15 January 2019
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**(+736)** . . N User:IssaRice/Subfield of math as study of concepts preserved under transformation (Created page with "See https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/ for an articulation of the general idea. Many of the examples are from Tao's post....") - 16:59, 10 January 2019
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**(+1,515)** . . N User:IssaRice/Distribution of X over Y (Created page with "A distribution of <math>X</math> over <math>Y</math> is any function <math>f : Y \to X</math>. Examples: * A probability distribution over a finite sample space is a distrib...") - 20:00, 9 January 2019
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**(+878)** . . N User:IssaRice/Computability and logic/K is recursively enumerable (Created page with "<math>K := \{x : x \in W_x\}</math> ==Proofs== ===Finding a partial recursive function that enumerates ''K''=== This proof is from Enderton.<ref>Herbert Enderton. ''Computa...") - 23:49, 8 January 2019 (diff | hist) . . (+130) . . N User:IssaRice/Linear algebra/Change of basis example in two dimensions (Created page with "This example comes from [https://www.youtube.com/watch?v=P2LTAUO1TdA&index=12&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab this video].")
- 22:20, 6 January 2019
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**(+903)** . . N User:IssaRice/Linear algebra/Matrix of a linear transformation (Created page with "==Notation== Axler writes <math>\mathcal M(T, (v_1,\ldots, v_n), (u_1, \ldots, u_m))</math>. Axler never abbreviates bases, although if he did, the notation would look like <...") (current) - 17:28, 6 January 2019
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**(+624)** . . N User:IssaRice/Linear algebra/Riesz representation theorem (Created page with "Let's take the case where <math>V = \mathbf R^n</math> and the inner product is the usual dot product. What does the Riesz representation theorem say in this case? It says tha...") - 15:34, 6 January 2019
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**(+762)** . . N User:IssaRice/Linear algebra/Invertible equals expressible as change of coordinate matrix (Created page with "Let <math>T : \mathbf F^n \to \mathbf F^n</math>. We want to write <math>T</math> as a change of coordinate matrix, i.e. as <math>[I]_\beta^{\beta'}</math> for some appropriat...") - 23:31, 2 January 2019 (diff | hist) . . (+475) . . N User:IssaRice/Linear algebra/Classification of operators (Created page with "Let <math>V</math> be a finite-dimensional inner product space, and let <math>T : V \to V</math> be a linear transformation. {| class="sortable wikitable" |- ! Operator name...")
- 21:35, 2 January 2019 (diff | hist) . . (+324) . . N User:IssaRice/Linear algebra/List of matrix products (Created page with "{| class="sortable wikitable" |- ! Product name !! Matrix notation !! Linear transformation/basis notation |- | || <math>QDQ^{-1}</math> where <math>Q</math> is invertible and...")
- 21:29, 2 January 2019 (diff | hist) . . (+91) . . N User:IssaRice/Properties of a list of vectors and their images (IssaRice moved page User:IssaRice/Properties of a list of vectors and their images to User:IssaRice/Linear algebra/Properties of a list of vectors and their images) (current)
- 21:28, 2 January 2019 (diff | hist) . . (+70) . . N User:IssaRice/Type checking vector spaces (IssaRice moved page User:IssaRice/Type checking vector spaces to User:IssaRice/Linear algebra/Type checking vector spaces) (current)
- 21:28, 2 January 2019 (diff | hist) . . (+68) . . N User:IssaRice/Outline of linear algebra (IssaRice moved page User:IssaRice/Outline of linear algebra to User:IssaRice/Linear algebra/Outline of linear algebra) (current)

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