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- 18:46, 14 June 2021 Commutator of x and Distributional Derivative acting on Distribution (hist | edit) [1,798 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $T \in \map {\DD'} \R$ be a distribution. Let: :$\sqbrk {x, \dfrac \d {\d x} } T := x \dfrac {\d T}{\d x} - \dfrac {\d \paren...")
- 03:02, 12 June 2021 Leigh.Samphier/Sandbox/Characterization of P-adic Valuation on Integers (hist | edit) [376 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == == Definition == Let $p \in \N$ be a prime number. Let $\nu_p^\Z: \Z \to \N \cup \set {+\infty}$ be the Definition...")
- 15:16, 9 June 2021 Excess Kurtosis of Logistic Distribution (hist | edit) [2,621 bytes] Robkahn131 (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $X$ be a continuous random variable which satisfies the Definition:Logistic Distribution|logistic...")
- 21:59, 6 June 2021 Equivalence Class Equivalent Statements/3 iff 6 (hist | edit) [628 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\RR$ be an equivalence relation on $S$. Let $x, y \in S$. {{TFAE}} :$x \mathrel \RR y$ :$\eqclass x \RR \cap \eqclas...")
- 21:58, 6 June 2021 Equivalence Class Equivalent Statements/3 iff 5 (hist | edit) [706 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\RR$ be an equivalence relation on $S$. Let $x, y \in S$. {{TFAE}} :$x \mathrel \RR y$ :$y \in \eqclass x \RR$ ==...")
- 21:56, 6 June 2021 Equivalence Class Equivalent Statements/3 iff 4 (hist | edit) [634 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\RR$ be an equivalence relation on $S$. Let $x, y \in S$. {{TFAE}} :$x \mathrel \RR y$ :$x \in \eqclass y \RR$ ==...")
- 21:53, 6 June 2021 Equivalence Class Equivalent Statements/2 iff 3 (hist | edit) [856 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\RR$ be an equivalence relation on $S$. Let $x, y \in S$. {{TFAE}} :$\eqclass x \RR = \eqclass y \RR$ :...")
- 21:48, 6 June 2021 Equivalence Class Equivalent Statements/1 iff 2 (hist | edit) [960 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\RR$ be an equivalence relation on $S$. Let $x, y \in S$. {{TFAE}} :$(1): \quad x$ and $y$ are in the same Definit...")
- 14:14, 6 June 2021 Right Operation Closed for All Subsets (hist | edit) [1,361 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set. Let $\rightarrow$ be the right operation on $S$. That is: :$\forall x, y \in S: x \rightar...")
- 14:14, 6 June 2021 Left Operation Closed for All Subsets (hist | edit) [1,360 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set. Let $\leftarrow$ be the left operation on $S$. That is: :$\forall x, y \in S: x \leftarrow...")
- 13:56, 6 June 2021 Image of P-adic Norm (hist | edit) [492 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the rationals $\Q$ for some Definiti...") originally created as "Leigh.Samphier/Sandbox/Image of P-adic Norm"
- 13:45, 6 June 2021 One-Step Subgroup Test/Linguistic Note (hist | edit) [463 bytes] Prime.mover (talk | contribs) (Created page with "== Linguistic Note on One-Step Subgroup Test == <onlyinclude> The '''One-Step Subgroup Test''' is so called despite the fact that, on the face of it, there are two ste...")
- 13:41, 6 June 2021 Two-Step Subgroup Test/Linguistic Note (hist | edit) [443 bytes] Prime.mover (talk | contribs) (Created page with "== Linguistic Note on Two-Step Subgroup Test == <onlyinclude> The Two-Step Subgroup Test is so called despite the fact that, on the face of it, there are three steps t...")
- 12:43, 6 June 2021 Thomae Function is Continuous at Irrational Numbers/Lemma (hist | edit) [3,253 bytes] Prime.mover (talk | contribs) (Created page with "== Lemma for Thomae Function is Continuous at Irrational Numbers == In the following it is to be understood that all rational numbers expre...")
- 07:35, 6 June 2021 Subsemigroup of Monoid is not necessarily Monoid (hist | edit) [1,653 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\struct {S, \circ}$ be a monoid whose identity is $e_S$. Let $\struct {T, \circ}$ be a Definition:...")
- 07:17, 6 June 2021 Identity of Submagma containing Identity of Magma is Same Identity (hist | edit) [1,271 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\struct {S, \circ}$ be a magma which has an identity $e$. Let $\struct {T, \circ}$ be a Definition:...")
- 06:23, 6 June 2021 Embedding Theorem/Corollary (hist | edit) [2,974 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let: :$(1): \quad \struct {T_2, \oplus_2, \otimes_2}$ be a submagma of $\struct {S_2, *_2, \star_2}$ :$(2): \quad f: \struct {T_1, \oplu...")
- 22:06, 5 June 2021 Embedding Theorem/Motivation (hist | edit) [1,027 bytes] Prime.mover (talk | contribs) (Created page with "== Motivation for Embedding Theorem == <onlyinclude> The following is a frequently occurring circumstance in the field of abstract algebra....")
- 20:46, 5 June 2021 Parity Group is Only Group with 2 Elements (hist | edit) [984 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\struct {G, \circ}$ be a group with exactly $2$ elements. Then $\struct {G, \circ}$ is Definition:Isomorphis...")
- 15:20, 5 June 2021 Smooth Real Function times Dirac Delta Distribution (hist | edit) [1,453 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $\alpha \in \map {\CC^\infty} \R$ be a smooth real function. Let $\delta \in \map {\DD'} \R$ be the Definition:Dirac...")
- 08:19, 5 June 2021 Real Numbers are Uncountably Infinite/Cantor's First Proof/Historical Note (hist | edit) [316 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Real Numbers are Uncountably Infinite: Cantor's First Proof == <onlyinclude> This proof wa...")
- 06:13, 5 June 2021 Invertible Element of Associative Structure is Cancellable/Corollary (hist | edit) [708 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\struct {S, \circ}$ be a monoid whose identity element is $e_S$. An Definition:Elemen...")
- 10:32, 4 June 2021 Transplanting Theorem/Corollary (hist | edit) [1,006 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\struct {S, \circ}$ be an algebraic structure. Let $f: S \to S$ be an Definition:Auto...")
- 22:25, 3 June 2021 Additive Group of Real Numbers is Not Isomorphic to Multiplicative Group of Real Numbers/Proof 3 (hist | edit) [1,642 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Additive Group of Real Numbers is Not Isomorphic to Multiplicative Group of Real Numbers}} == Proof == <onlyinclude> There are two Definition:Element|eleme...")
- 21:57, 3 June 2021 Coordinate Representation of Laplace-Beltrami Operator (hist | edit) [895 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $\struct {M, g}$ be a Riemannian manifold. Let $U \subseteq M$ be an open set. Let $\tuple {x^i...")
- 21:46, 3 June 2021 Coordinate Representation of Divergence (hist | edit) [900 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $\struct {M, g}$ be a Riemannian manifold. Let $U \subseteq M$ be an open set. Let $\paren {x^i...")
- 21:15, 3 June 2021 Fundamental Solution to Nth Derivative (hist | edit) [2,400 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $H$ be the Heaviside step function. Let $n \in \N_{\mathop > 0}$. Let $\ds \map {f_n} x = \map H x \frac {x^{n - 1}...")
- 22:00, 1 June 2021 Count of Commutative Binary Operations with Fixed Identity/Sequence (hist | edit) [788 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set whose cardinality is $n$. Let $x \in S$. Let $N$ denote the number of different Definition:Co...")
- 21:56, 1 June 2021 Count of Binary Operations Without Identity/Sequence (hist | edit) [852 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set whose cardinality is $n$. Let $N$ denote the number of different Definition:Binary Operation|b...")
- 21:51, 1 June 2021 Count of Commutative Binary Operations with Identity/Sequence (hist | edit) [772 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set whose cardinality is $n$. Let $N$ denote the number of different Definition:Commutative Operat...")
- 21:40, 1 June 2021 Count of Binary Operations with Fixed Identity/Sequence (hist | edit) [689 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set whose cardinality is $n$. Let $x \in S$. The number $N$ of possible different Definition:Bina...")
- 20:45, 1 June 2021 Inverse Element/Examples/Multiplication Modulo 6 (hist | edit) [822 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Inverse Elements == <onlyinclude> Consider the '''Definition:Multiplicative Monoid of Integers Modulo m|multiplicative monoid o...")
- 20:43, 1 June 2021 Inverse Element/Examples/Addition Modulo 6 (hist | edit) [763 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Inverse Elements == <onlyinclude> Consider the '''Definition:Additive Group of Integers Modulo m|additive group of integers mod...")
- 09:41, 1 June 2021 Inverse Element/Examples/Symmetry Group of Square (hist | edit) [706 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Inverse Elements == <onlyinclude> Consider the '''symmetry group of the square''': {{:De...")
- 09:32, 1 June 2021 Inverse Element/Examples (hist | edit) [544 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Inverse Elements == <onlyinclude> === Symmetry Group of Square === {{:Inver...")
- 06:34, 1 June 2021 Identity/Examples/Symmetry Group of Square (hist | edit) [643 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Identity Element == <onlyinclude> Consider the '''symmetry group of the square''': {{:De...")
- 22:12, 31 May 2021 Set Difference with Set Difference is Union of Set Difference with Intersection/Venn Diagram (hist | edit) [1,250 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Set Difference with Set Difference is Union of Set Difference with Intersection}} == Proof == Demonstration by Venn diagram: <on...")
- 21:46, 31 May 2021 Set Difference with Union/Venn Diagram (hist | edit) [1,195 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Set Difference is Right Distributive over Set Intersection}} == Proof == Demonstration by Venn diagram: <onlyinclude> :File:Se...")
- 21:35, 31 May 2021 Set Difference is Right Distributive over Set Intersection/Venn Diagram (hist | edit) [1,209 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Set Difference is Right Distributive over Set Intersection}} == Proof == Demonstration by Venn diagram: <onlyinclude> :File:Se...")
- 17:44, 31 May 2021 Fundamental Solution to y'' + w y (hist | edit) [3,138 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $H$ be the Heaviside step function. Let $\omega \in \R : \omega \ne 0$. Let $\ds \map f x = \map H x \frac {\map \s...")
- 16:28, 31 May 2021 Electron Charge to Mass Ratio (hist | edit) [5,263 bytes] Prime.mover (talk | contribs) (Created page with "== Physical Law == The ratio of the charge to the mass of an Definition:Electron|elec...")
- 15:23, 31 May 2021 Electron Charge to Mass Ratio/Historical Note (hist | edit) [974 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Electron Charge to Mass Ratio == <onlyinclude> When an electrode is charged to a high Defin...")
- 11:59, 31 May 2021 De Morgan's Laws (Set Theory)/Set Difference/Difference with Intersection/Venn Diagram (hist | edit) [1,165 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:De Morgan's Laws (Set Theory)/Set Difference/Difference with Intersection}} == Proof == Demonstration by Venn diagram: <onlyincl...")
- 11:48, 31 May 2021 De Morgan's Laws (Set Theory)/Set Difference/Difference with Union/Venn Diagram (hist | edit) [1,620 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:De Morgan's Laws (Set Theory)/Set Difference/Difference with Union}} == Proof == Demonstration by Venn diagram: <onlyinclude> :[...")
- 11:14, 31 May 2021 De Morgan's Laws (Set Theory)/Relative Complement/Complement of Union/Proof 2 (hist | edit) [2,403 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:De Morgan's Laws (Set Theory)/Relative Complement/Complement of Union}} == Proof == <onlyinclude> Let $x \in S$ througout. {{begin-eqn}} {{eqn | o =...")
- 10:57, 31 May 2021 De Morgan's Laws (Set Theory)/Relative Complement/Complement of Union/Proof 1 (hist | edit) [753 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:De Morgan's Laws (Set Theory)/Relative Complement/Complement of Union}} == Proof == <onlyinclude> Let $T_1, T_2 \subseteq S$. Then from Union is Smallest...")
- 21:02, 30 May 2021 Equivalence of Definitions of Modulo Multiplication (hist | edit) [4,804 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{TFAE|def = Modulo Multiplication}} === Definition 1 === {{:Definition:Modulo Multiplication/Definition 1}}...")
- 20:52, 30 May 2021 Equivalence of Definitions of Integer Modulo Addition (hist | edit) [4,642 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{TFAE|def = Modulo Addition}} === Definition 1 === {{:Definition:Modulo Addition/Definition 1}} === Definition:M...")
- 16:23, 30 May 2021 Fundamental Solution to Reduced Linear First Order ODE with Constant Coefficients (hist | edit) [1,998 bytes] Julius (talk | contribs) (Created page with "== Theorem == Let $H$ be the Heaviside step function. Let $\map f x = \map H x \map \exp {\lambda x}$. Let $T_f$ be the Definition:...") originally created as "Fundamental Solution to Linear First Order ODE with Constant Coefficients"
- 14:35, 30 May 2021 Operation/Examples/Multiplication (hist | edit) [618 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Operation == <onlyinclude> An example of an operation from conventional arithmetic is...")