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- 10:28, 24 August 2019 Leigh.Samphier/Sandbox/Left Module Does Not Necessarily Induce Right Module over Ring (hist) [1,258 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\struct {R, +_R, \times_R}$ be a ring. Let $\struct{G, +_G, \circ}$ be a Definition:Left Module|le...")
- 03:43, 24 August 2019 Integration by Inversion (hist) [1,100 bytes] Prime.mover (talk | contribs) (Appeared in my twitter feed from math prof this morning. Thought it was neat.)
- 12:40, 23 August 2019 L'Hôpital's Rule/Examples/(Root of (1 plus x) minus 1) over x (hist) [1,377 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Use of L'Hôpital's Rule == <onlyinclude> :$\displaystyle \lim_{x \mathop \to 0} \dfrac {\sqrt {1 + x} - 1} x = \dfrac 1 2$ </onlyinclude> == Proof == Let...")
- 12:21, 23 August 2019 L'Hôpital's Rule/Examples (hist) [308 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of L'Hôpital's Rule == <onlyinclude> === Example: $\dfrac {\sqrt {1 - x} - 1} x$ ==...")
- 10:46, 23 August 2019 Hero's Method/Examples/5 (hist) [1,260 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Hero's Method == <onlyinclude> The calculation of the square root of $5$ by Hero's Method proceeds as follows: {{begi...")
- 10:27, 23 August 2019 Hero's Method/Examples (hist) [203 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Hero's Method == <onlyinclude> </onlyinclude> Category:Examples of Use of Hero's Method")
- 08:48, 22 August 2019 Leigh.Samphier/Sandbox/Definition:Module (hist) [4,735 bytes] Leigh.Samphier (talk | contribs) (Created page with "== Definition == <onlyinclude> Let $\struct {R, +_R, \times_R}$ be a ring. Let $\struct {G, +_G}$ be an Definition:Abelian Group|abel...")
- 07:16, 22 August 2019 Leigh.Samphier/Sandbox/Left Ideal is Left Module over Ring/Ring is Left Module over Ring (hist) [820 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\struct {R, +, \times}$ be a ring. Then $\struct {R, +, \times}$ is a Definition:Left Module|left...")
- 07:14, 22 August 2019 Leigh.Samphier/Sandbox/Right Ideal is Right Module over Ring/Ring is Right Module over Ring (hist) [827 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\struct {R, +, \times}$ be a ring. Then $\struct {R, +, \times}$ is a Definition:Right Module|rig...")
- 03:13, 22 August 2019 Acceleration Due to Gravity/Earth's Surface (hist) [930 bytes] Prime.mover (talk | contribs) (Created page with "== Physical Law == Let a body $B$ be situated in a uniform gravitational field $M$ given rise to by a Definition:Body...")
- 03:06, 22 August 2019 Acceleration Due to Gravity/Historical Note (hist) [1,035 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Acceleration Due to Gravity == <onlyinclude> This result famously contradicts {{AuthorRef|Aristotle}}, who taught that heavier objects fall faster th...")
- 12:58, 21 August 2019 Basel Problem/Proof 10 (hist) [2,586 bytes] Caliburn (talk | contribs) (Created page with "== Theorem == {{:Basel Problem}} == Proof == <onlyinclude> From Mittag-Leffler Expansion for Hyperbolic Cotangent Function, we have: :$\displaystyle \frac 1 {2 z} \pare...")
- 01:37, 21 August 2019 Construction of Fermat Point (hist) [1,182 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\triangle ABC$ be a triangle Let the vertices of $\triangle ABC$ all have Definitio...")
- 01:14, 21 August 2019 Euler Polyhedron Formula/Examples/Tetrahedron (hist) [793 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Euler Polyhedron Formula == <onlyinclude> The cube has: :$4$ vertices :$6$ Definitio...")
- 01:11, 21 August 2019 Euler Polyhedron Formula/Examples/Cube (hist) [789 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Euler Polyhedron Formula == <onlyinclude> The cube has: :$8$ vertices :$12$ Defi...")
- 01:05, 21 August 2019 Euler Polyhedron Formula/Examples (hist) [361 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Use of Euler Polyhedron Formula == <onlyinclude> === Tetrahedron === {{:Euler Polyhedron Formula/Examples/...")
- 02:05, 20 August 2019 Doubling the Cube/Historical Note/Mistake (hist) [1,146 bytes] Prime.mover (talk | contribs) (Created page with "== Source Work == {{BookReference|Curious and Interesting Numbers|1986|David Wells}}: :The Dictionary ::$2$ == Mistake == <onlyinclude> :''The legend was told that the Athe...")
- 18:44, 18 August 2019 Ceva's Theorem (hist) [4,193 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\triangle ABC$ be a triangle. Let $L$, $M$ and $N$ be points on the Definition:Side of Polygon|s...")
- 07:55, 18 August 2019 Cayley's Theorem (Category Theory)/Historical Note (hist) [1,098 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Cayley's Theorem (Category Theory) == <onlyinclude> Although {{AuthorRef|Arthur Cayley|Cayley}} did not prove this result, it is similar enough in bo...")
- 07:43, 18 August 2019 Cayley's Representation Theorem/Also known as (hist) [384 bytes] Prime.mover (talk | contribs) (Created page with "== Cayley's Representation Theorem: Also known as == <onlyinclude> '''Cayley's Representation Theorem''' is also known as the '''Representation Theorem for Groups'''....")
- 03:20, 18 August 2019 Cauchy-Bunyakovsky-Schwarz Inequality for Definite Integrals/Historical Note (hist) [407 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Cauchy-Bunyakovsky-Schwarz Inequality for Definite Integrals == <onlyinclude> The Cauchy-Bunyakovsky-Schwarz Inequality for Definite Integrals wa...")
- 19:22, 17 August 2019 Leigh.Samphier/Sandbox/Right Ideal is Right Module over Ring (hist) [1,622 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\struct {R, +, \times}$ be a ring. Let $J \subseteq R$ be a right ideal o...")
- 19:13, 17 August 2019 Leigh.Samphier/Sandbox/Left Ideal is Left Module over Ring (hist) [1,634 bytes] Leigh.Samphier (talk | contribs) (Created page with "{{Proofread}} == Theorem == Let $\struct {R, +, \times}$ be a ring. Let $J \subseteq R$ be a left ideal of...")
- 18:15, 17 August 2019 Cantor's Diagonal Argument/Historical Note (hist) [305 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Cantor's Diagonal Argument == <onlyinclude> {{AuthorRef|Georg Cantor}} was the first on record to have used the technique of what is now referred to...")
- 13:35, 16 August 2019 Equality of Squares Modulo Integer is Equivalence Relation (hist) [474 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $n \in \Z_{>0}$ be a (strictly) positive integer. Let $\mathcal R_n$ be the relation o...")
- 12:06, 16 August 2019 Exists Divisor in Set of n+1 Natural Numbers no greater than 2n (hist) [2,553 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ be a set of $n + 1$ non-non-zero natural numbers all less than or equal to...")
- 02:25, 16 August 2019 Equivalence Relation on Natural Numbers such that Quotient is Power of Two/One of Pair of Equivalent Elements is Divisor of the Other (hist) [1,561 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\alpha$ denote the relation defined on the natural numbers $\N$ by: :$\forall x, y \in \N: x \mathre...")
- 02:07, 16 August 2019 Equivalence Relation on Natural Numbers such that Quotient is Power of Two/Equivalence Class Contains 1 Odd Number (hist) [3,048 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\alpha$ denote the relation defined on the natural numbers $\N$ by: :$\forall x, y \in \N: x \mathre...")
- 01:44, 16 August 2019 Number of Friday 13ths in a Year (hist) [1,839 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == In any given year, there are between $1$ and $3$ (inclusive) months in which the $13$th falls on a Friday. == Proof == The day of the we...")
- 18:26, 15 August 2019 Equivalence Class/Examples/Months that Start on the Same Day of the Week (hist) [3,222 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Equivalence Relation == <onlyinclude> Let $M$ be the set of months of the Definitio...")
- 17:45, 15 August 2019 Equivalence Relation/Examples/Months that Start on the Same Day of the Week (hist) [2,170 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Equivalence Relation == <onlyinclude> Let $M$ be the set of months of the Definitio...")
- 17:29, 15 August 2019 Symmetric and Transitive Relation is not necessarily Reflexive/Proof 3 (hist) [1,557 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Symmetric and Transitive Relation is not necessarily Reflexive}} == Proof == <onlyinclude> Proof by Counterexample: Let $S = \set {1, 2}$ be a Definit...")
- 02:34, 15 August 2019 Set Partition/Examples/Partition into Singletons (hist) [838 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Set Partition == <onlyinclude> Let $S$ be a set. Consider the Definition:Indexed Family of Subsets|family of s...")
- 17:53, 14 August 2019 Existence of Bijection between Coproducts of two Sets (hist) [1,396 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S_1$ and $S_2$ be sets. Let $\struct {C, i_1, i_2}$ and $\struct {D, j_1, j_2}$ be two coproducts on $S_1$...")
- 17:23, 14 August 2019 Coproduct on Disjoint Union (hist) [2,970 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S_1$ and $S_2$ be sets. Let $S_1 \sqcup S_2 := \paren {S_1 \times \set 1} \cup \paren {S_2 \times \set 2}$ be the Definition:Disjoint...")
- 02:44, 14 August 2019 Component Mappings of Set Coproduct are Injective (hist) [1,333 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S_1$ and $S_2$ be sets. Let $\struct {C, i_1, i_2}$ be a coproduct of $S_1$ and $S_2$. Then $i_1$ and $i...")
- 02:05, 14 August 2019 Composite of Three Mappings in Cycle forming Injections and Surjection (hist) [2,881 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $A$, $B$ and $C$ be non-empty sets. Let $f: A \to B$, $g: B \to C$ and $h: C \to A$ be Definition:Mapping...")
- 18:17, 13 August 2019 Composition of 3 Mappings where Pairs of Mappings are Bijections (hist) [3,374 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $A$, $B$, $C$ and $D$ be sets. Let: :$f: A \to B$ :$g: B \to C$ :$h: C \to D$ be mappings. Let $g \circ f$ and $...")
- 16:03, 13 August 2019 Real Square Function is neither Injective nor Surjective (hist) [1,161 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Mapping which is Not an Injection nor a Surjection == <onlyinclude> Let $f: \R \to \R$...")
- 15:53, 13 August 2019 Graph of Real Bijection in Coordinate Plane intersects Horizontal Line at One Point (hist) [2,084 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: \R \to \R$ be a real function which is bijective. Let its graph b...")
- 15:43, 13 August 2019 Graph of Real Injection in Coordinate Plane intersects Horizontal Line at most Once (hist) [2,018 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: \R \to \R$ be a real function which is injective. Let its graph b...")
- 15:36, 13 August 2019 Graph of Real Surjection in Coordinate Plane intersects Every Horizontal Line (hist) [1,816 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: \R \to \R$ be a real function which is surjective. Let its graph...")
- 03:04, 13 August 2019 Equation of Horizontal Line (hist) [1,893 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\mathcal L$ be a horizontal line embedded in the Cartesian plane $\mathcal C$. Then the D...")
- 02:49, 13 August 2019 Equation of Vertical Line (hist) [1,696 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\mathcal L$ be a vertical line embedded in the Cartesian plane $\mathcal C$. Then the Defin...")
- 02:21, 13 August 2019 Graph of Real Function in Coordinate Plane intersects Vertical at One Point (hist) [1,547 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: \R \to \R$ be a real function. Let its graph be embedded in the Definition:Cartesian Pla...")
- 17:27, 12 August 2019 Direct Image of Intersection with Inverse Image (hist) [3,008 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $S$ and $T$ be sets. Let $f: S \to T$ be a mapping. Let: :$f^\to: \powerset S \to \powerset T$ denote the Defi...")
- 16:43, 12 August 2019 Inverse Image of Direct Image of Inverse Image equals Inverse Image Mapping (hist) [2,203 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: S \to T$ be a mapping. Let: :$f^\to: \powerset S \to \powerset T$ denote the Definition:Direct Image Mapping of Mapping|direct...")
- 16:42, 12 August 2019 Direct Image of Inverse Image of Direct Image equals Direct Image Mapping (hist) [2,221 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f: S \to T$ be a mapping. Let: :$f^\to: \powerset S \to \powerset T$ denote the Definition:Direct Image Mapping of Mapping|direct...")
- 15:28, 12 August 2019 Complement of Direct Image Mapping of Injection equals Direct Image of Complement (hist) [1,658 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f: S \to T$ be an injection. Let $f^\to: \powerset S \to \powerset T$ denote the Definition:Direct Image Mapping o...")
- 11:25, 12 August 2019 Laplace Transform of Exponential times Cosine (hist) [1,027 bytes] Caliburn (talk | contribs) (Created page with "== Theorem == <onlyinclude> :$\map {\laptrans {e^{b t} \cos a t} } s = \dfrac {s - b} {\paren {s - b}^2 + a^2}$ </onlyinclude> where: :$a$ and $b$ are Definition:Real Number...")