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26 April 2024
| 04:25 | User talk:Prime.mover diffhist +232 Asdfghjklohhnhn talk contribs | ||||
| N 03:00 | Limit to Infinity of Binomial Coefficient over Power/Proof 2 diffhist +1,573 CircuitCraft talk contribs (Created page with "== Theorem == {{:Limit to Infinity of Binomial Coefficient over Power}} == Proof == <onlyinclude> This proof applies to the special case where $k \in \Z$. Then, {{hypothesis}}, we need only consider: :$k \in \set {0, 1, 2, \dotsc}$ By Gamma Function Extends Factorial, it suffices to show: :$\ds \lim_{r \mathop \to \infty} \frac {\dbinom r k} {r^k} = \frac 1 {k !}$ We have: {{begin-eqn}} {{eqn | q = \forall r \in \R | l = \frac {\dbinom r k} {r^k} |...") | ||||
| m 02:41 | Definition:Power (Algebra)/Integer diffhist 0 CircuitCraft talk contribs | ||||
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02:34 | Limit to Infinity of Binomial Coefficient over Power 2 changes history −1,378 [CircuitCraft (2×)] | |||
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02:34 (cur | prev) +59 CircuitCraft talk contribs | ||||
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02:14 (cur | prev) −1,437 CircuitCraft talk contribs | ||||
| m 02:16 | Definition:Binomial Coefficient/Real Numbers diffhist 0 CircuitCraft talk contribs | ||||
| N 02:14 | Limit to Infinity of Binomial Coefficient over Power/Proof 1 diffhist +1,855 CircuitCraft talk contribs (Created page with "== Theorem == {{:Limit to Infinity of Binomial Coefficient over Power}} == Proof == <onlyinclude> {{begin-eqn}} {{eqn | l = \lim_{r \mathop \to \infty} \frac {\dbinom r k} {r^k} | r = \lim_{r \mathop \to \infty} \frac {\map \Gamma {r + 1} } {\map \Gamma {k + 1} \map \Gamma {r - k + 1} r^k} | c = Gamma Function Extends Factorial }} {{eqn | r = \lim_{r \mathop \to \infty} \frac 1 {\map \Gamma {k + 1} } \frac {\sqrt {2 \pi r} \paren {r / e}^r} {\sqrt {2 \p...") | ||||
25 April 2024
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23:49 | Definition:Isometry 5 changes history +584 [Prime.mover (5×)] | |||
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23:49 (cur | prev) +231 Prime.mover talk contribs | ||||
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23:44 | Definition:Isometry (Riemannian Manifolds) 2 changes history +326 [Prime.mover (2×)] | |||
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23:44 (cur | prev) −2 Prime.mover talk contribs | |||
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09:54 (cur | prev) +328 Prime.mover talk contribs | ||||
| Nm 23:40 | User talk:Sabaday diffhist +1,240 Prime.mover talk contribs (Welcome!) | ||||
| Nm 23:40 | User:Sabaday diffhist +76 Prime.mover talk contribs (Creating user page for new user.) | ||||
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23:40 | (User creation log) [Prime.mover (2×)] | |||
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23:40 User account Sabaday talk contribs was created by Prime.mover talk contribs and password was sent by email | ||||
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07:07 User account Wikimiki talk contribs was created by Prime.mover talk contribs and password was sent by email | ||||
| 11:59 | Category:Examples of Isometries diffhist +16 Prime.mover talk contribs | ||||
| 11:59 | Category:Metric Space Completeness is Preserved by Isometry diffhist +37 Prime.mover talk contribs | ||||
| 11:58 | Category:Isometry Preserves Sequence Convergence diffhist +37 Prime.mover talk contribs | ||||
| 11:57 | Isometry Preserves Sequence Convergence diffhist +16 Prime.mover talk contribs | ||||
| m 11:57 | Isometric Image of Cauchy Sequence is Cauchy Sequence diffhist +16 Prime.mover talk contribs | ||||
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m 11:56 | Definition:Isolated Singularity/Complex Function 2 changes history +517 [Prime.mover (2×)] | |||
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11:56 (cur | prev) +446 Prime.mover talk contribs | |||
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08:02 (cur | prev) +71 Prime.mover talk contribs | |||
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N 11:40 | User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Rank Axioms/Formulation 1 Implies Formulation 2 2 changes history +1,112 [Leigh.Samphier (2×)] | |||
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11:40 (cur | prev) +63 Leigh.Samphier talk contribs | ||||
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11:34 (cur | prev) +1,049 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\rho : \powerset S \to \Z$ be a mapping from the power set of $S$ to the integers. Let $\rho$ satisfy formulation 1 of the rank axioms: {{:Axiom:Rank Axioms (Matroid)/Definition 1}} Then $\rho$ is the Definition:Rank Function (Matroid)...") | |||
| N 11:29 | User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Rank Axioms/Formulation 2 Implies Formulation 1 diffhist +3,250 Leigh.Samphier talk contribs (Created page with "{{Proofread}} == Theorem == Let $S$ be a finite set. Let $\rho : \powerset S \to \Z$ be a mapping from the power set of $S$ to the integers. Let $\rho$ satisfy formulation 2 of the rank axioms: {{:Axiom:Rank Axioms (Matroid)/Definition 2}} Then $\rho$ satisfies Axiom:Rank Axioms (Matroid)/Def...") | ||||
| 11:21 | User:Leigh.Samphier/Matroids diffhist +240 Leigh.Samphier talk contribs | ||||
| 10:51 | Deletion log Prime.mover talk contribs deleted page Completion Theorem/Normed Vector Space (content was: "#REDIRECT Completion Theorem (Normed Vector Space)", and the only contributor was "Prime.mover" (talk)) | ||||
| m 10:48 | Definition:Isometric Isomorphism/Normed Division Ring diffhist +124 Prime.mover talk contribs | ||||
| m 10:46 | Equivalence Class of Isometries is Subset of Equivalence Class of Homeomorphisms diffhist +16 Prime.mover talk contribs | ||||
| m 10:45 | Isometry is Homeomorphism of Induced Topologies diffhist +16 Prime.mover talk contribs | ||||
| 10:44 | Metric Space Completeness is Preserved by Isometry diffhist +16 Prime.mover talk contribs | ||||
| m 10:44 | Isometry of Metric Spaces is Homeomorphism diffhist +16 Prime.mover talk contribs | ||||
| m 10:44 | Isometry of Metric Spaces is Equivalence Relation diffhist +16 Prime.mover talk contribs | ||||
| 10:43 | Isometry between Metric Spaces is Continuous/Corollary diffhist +34 Prime.mover talk contribs | ||||
| N 10:43 | Category:Isometry between Metric Spaces is Continuous diffhist +60 Prime.mover talk contribs (Created page with "{{Result-category}} Category:Isometries (Metric Spaces)") | ||||
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10:43 | Isometry between Metric Spaces is Continuous 2 changes history +100 [Prime.mover (2×)] | |||
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10:43 (cur | prev) +84 Prime.mover talk contribs | ||||
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10:41 (cur | prev) +16 Prime.mover talk contribs | |||
| m 10:41 | Isometric Metric Spaces are Homeomorphic diffhist +16 Prime.mover talk contribs | ||||
| m 10:41 | Equivalence of Definitions of Isometry of Metric Spaces diffhist +16 Prime.mover talk contribs | ||||
| m 10:40 | Homeomorphic Metric Spaces are not necessarily Isometric diffhist +16 Prime.mover talk contribs | ||||
| m 10:40 | Distance-Preserving Surjection is Isometry of Metric Spaces diffhist +16 Prime.mover talk contribs | ||||
| m 10:39 | Normed Division Ring Completions are Isometric and Isomorphic/Lemma 4 diffhist +32 Prime.mover talk contribs | ||||
| m 10:39 | Normed Division Ring Completions are Isometric and Isomorphic/Lemma 5 diffhist +48 Prime.mover talk contribs | ||||
| m 10:38 | Normed Division Ring Completions are Isometric and Isomorphic/Lemma 3 diffhist +16 Prime.mover talk contribs | ||||
| 10:38 | Normed Division Ring Completions are Isometric and Isomorphic/Lemma 2 diffhist +16 Prime.mover talk contribs | ||||
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m 10:36 | Riemannian Volume Form under Orientation-Preserving Isometry 2 changes history +96 [Prime.mover (2×)] | |||
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10:36 (cur | prev) +1 Prime.mover talk contribs | |||
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10:36 (cur | prev) +95 Prime.mover talk contribs | |||
| 10:35 | Smooth Mapping between Equidimensional Riemannian Manifolds is Local Isometry iff it is Isometry diffhist +76 Prime.mover talk contribs | ||||
| 10:34 | Definition:Flat Riemannian Manifold diffhist +94 Prime.mover talk contribs | ||||
| 10:33 | Distance-Preserving Image Isometric to Domain for Metric Spaces diffhist +74 Prime.mover talk contribs | ||||
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10:30 | Definition:Isometry (Hilbert Spaces) 2 changes history +437 [Prime.mover (2×)] | |||
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10:30 (cur | prev) −1 Prime.mover talk contribs | |||
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10:30 (cur | prev) +438 Prime.mover talk contribs | ||||
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10:25 | Definition:Local Isometry 3 changes history +281 [Prime.mover (3×)] | |||
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10:24 (cur | prev) +3 Prime.mover talk contribs | |||
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10:24 (cur | prev) +278 Prime.mover talk contribs | ||||
| N 10:21 | Category:Definitions/Linear Isometries diffhist +76 Prime.mover talk contribs (Created page with "{{DefinitionCategory|def = Linear Isometry|Normed Vector Spaces|Isometries}}") | ||||
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10:21 | Definition:Linear Isometry 2 changes history +76 [Prime.mover (2×)] | |||
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10:21 (cur | prev) +20 Prime.mover talk contribs | ||||
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10:20 (cur | prev) +56 Prime.mover talk contribs | ||||
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10:19 | Definition:Isometry of Riemannian Manifold 2 changes history +120 [Prime.mover (2×)] | |||
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10:19 (cur | prev) +23 Prime.mover talk contribs | ||||
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10:19 (cur | prev) +97 Prime.mover talk contribs | ||||
| 10:18 | Definition:Isometry Group of Riemannian Manifold diffhist +76 Prime.mover talk contribs | ||||
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N 10:15 | Completion Theorem 3 changes history +352 [Prime.mover (3×)] | |||
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10:15 (cur | prev) +27 Prime.mover talk contribs | ||||
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10:14 (cur | prev) +33 Prime.mover talk contribs | ||||
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10:14 (cur | prev) +292 Prime.mover talk contribs (Created page with "{{Disambiguation}} === Completion Theorem (Metric Space) === {{:Completion Theorem (Metric Space)}} === Completion Theorem (Measure Space) === {{:Completion Theorem (Measure Space)}} === Completion Theorem (Normed Vector Space) === {{:Completion Theorem (Normed Vector Space)}}") | |||
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10:15 | Category:Completion Theorem 2 changes history +5 [Prime.mover (2×)] | |||
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10:15 (cur | prev) +43 Prime.mover talk contribs | ||||
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10:03 (cur | prev) −38 Prime.mover talk contribs (Removed redirect to Category:Completion Theorem (Metric Space)) Tag: Removed redirect | ||||
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10:13 | Completion Theorem (Metric Space) 3 changes history +62 [Prime.mover (3×)] | |||
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10:13 (cur | prev) +4 Prime.mover talk contribs | ||||
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10:00 (cur | prev) +15 Prime.mover talk contribs | ||||
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09:59 (cur | prev) +43 Prime.mover talk contribs | ||||
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N 10:12 | Category:Completion Theorem (Measure Space) 2 changes history +89 [Prime.mover (2×)] | |||
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10:12 (cur | prev) +9 Prime.mover talk contribs | ||||
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10:11 (cur | prev) +80 Prime.mover talk contribs (Created page with "{{Result-category}} Category:Measure Spaces Category:Completion Theorem") | |||
| 10:12 | Completion Theorem (Measure Space)/Lemma diffhist −21 Prime.mover talk contribs | ||||
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10:10 | Category:Completion Theorem (Metric Space) 3 changes history +41 [Prime.mover (3×)] | |||
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10:10 (cur | prev) +4 Prime.mover talk contribs | ||||
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10:01 (cur | prev) +16 Prime.mover talk contribs | ||||
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10:00 (cur | prev) +21 Prime.mover talk contribs | ||||
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10:09 | (Move log) [Prime.mover (4×)] | |||
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10:09 Prime.mover talk contribs moved page Completion Theorem/Normed Vector Space to Completion Theorem (Normed Vector Space) | ||||
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09:59 Prime.mover talk contribs moved page Category:Completion Theorem to Category:Completion Theorem (Metric Space) | ||||
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08:42 Prime.mover talk contribs moved page Category:Isometries to Category:Isometries (Metric Spaces) | ||||
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08:41 Prime.mover talk contribs moved page Category:Definitions/Isometries to Category:Definitions/Isometries (Metric Spaces) | ||||
| N 10:09 | Category:Completion Theorem (Normed Vector Space) diffhist +86 Prime.mover talk contribs (Created page with "{{Result-category}} Category:Normed Vector Spaces Category:Completion Theorem") | ||||
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10:05 | Completion Theorem (Measure Space) 2 changes history +79 [Prime.mover (2×)] | |||
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10:05 (cur | prev) +52 Prime.mover talk contribs | ||||
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10:05 (cur | prev) +27 Prime.mover talk contribs | ||||
| 10:03 | Completion Theorem (Metric Space)/Lemma 3 diffhist +15 Prime.mover talk contribs | ||||
| m 10:02 | Completion Theorem (Metric Space)/Lemma 2 diffhist +15 Prime.mover talk contribs | ||||
| m 10:02 | Completion Theorem (Metric Space)/Lemma 1 diffhist +15 Prime.mover talk contribs | ||||
| m 10:01 | Completion Theorem (Metric Space)/Lemma 4 diffhist +15 Prime.mover talk contribs | ||||
| 09:58 | Category:Isometries diffhist +7 Prime.mover talk contribs (Removed redirect to Category:Isometries (Metric Spaces)) | ||||
| 09:57 | Category:Definitions/Isometries diffhist −10 Prime.mover talk contribs (Removed redirect to Category:Definitions/Isometries (Metric Spaces)) | ||||
| N 09:55 | Category:Isometries (Riemannian Manifolds) diffhist +193 Prime.mover talk contribs (Created page with "{{SubjectCategory|Isometry (Riemannian Manifolds)|disp = isometries|context = Riemannian Manifold|contextdisp = Riemannian manifolds}} Category:Riemannian Manifolds Category:Isometries") | ||||
| N 09:55 | Category:Definitions/Isometries (Riemannian Manifolds) diffhist +175 Prime.mover talk contribs (Created page with "{{DefinitionCategory|def = Isometry (Riemannian Manifolds)|disp = isometries|context = Riemannian Manifold|contextdisp = Riemannian manifolds|Riemannian Manifolds|Isometries}}") | ||||
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09:50 | Definition:Isometry (Inner Product Spaces) 2 changes history +328 [Prime.mover (2×)] | |||
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09:50 (cur | prev) −1 Prime.mover talk contribs | ||||
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09:48 (cur | prev) +329 Prime.mover talk contribs | ||||
| N 09:50 | Category:Definitions/Isometries (Inner Product Spaces) diffhist +175 Prime.mover talk contribs (Created page with "{{DefinitionCategory|def = Isometry (Inner Product Spaces)|disp = isometries|context = Inner Product Space|contextdisp = inner product spaces|Inner Product Spaces|Isometries}}") | ||||
| N 09:50 | Category:Isometries (Inner Product Spaces) diffhist +193 Prime.mover talk contribs (Created page with "{{SubjectCategory|Isometry (Inner Product Spaces)|disp = isometries|context = Inner Product Space|contextdisp = inner product spaces}} Category:Inner Product Spaces Category:Isometries") | ||||
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09:48 | Category:Isometries (Metric Spaces) 2 changes history +69 [Prime.mover (2×)] | |||
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09:48 (cur | prev) +24 Prime.mover talk contribs | ||||
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09:47 | Category:Definitions/Isometries (Metric Spaces) 3 changes history +29 [Prime.mover (3×)] | |||
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09:47 | Definition:Isometry (Metric Spaces) 4 changes history −91 [Prime.mover (4×)] | |||
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| 09:24 | Definition:Isometry (Metric Spaces)/Definition 1 diffhist +125 Prime.mover talk contribs | ||||
| 09:01 | Definition:Isometry (Metric Spaces)/Into diffhist +211 Prime.mover talk contribs | ||||
| 09:00 | Definition:Isometry (Metric Spaces)/Definition 2 diffhist +84 Prime.mover talk contribs | ||||
| N 08:57 | Definition:Isometry (Metric Spaces)/Also defined as diffhist +513 Prime.mover talk contribs (Created page with "== Isometry in the context of Metric Spaces: Also defined as == <onlyinclude> Some sources do not insist that an '''isometry''' be surjective. Make sure to know which prerequisites are used when quoting results about '''isometries'''. </onlyinclude> == Sources == {{SourceReview}} Category:De...") | ||||
| 08:54 | Definition:Metric Equivalence diffhist +13 Prime.mover talk contribs | ||||
| 08:54 | Definition:Isometric Metric Spaces diffhist +52 Prime.mover talk contribs | ||||
| N 08:53 | Definition:Metrically Equivalent Spaces diffhist +102 Prime.mover talk contribs (Redirected page to Definition:Isometry (Metric Spaces)) | ||||
| N 08:53 | Definition:Isometry (Metric Spaces)/Also known as diffhist +816 Prime.mover talk contribs (Created page with "== Isometry in the context of Metric Spaces: Also known as == <onlyinclude> An '''isometry''' is also known as a '''metric equivalence'''. Two '''isometric spaces''' can also be referred to as '''metrically equivalent'''. Texts which approach the...") | ||||
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m 08:34 | Acnode/Examples/Policeman on Point Duty 2 changes history +18 [Prime.mover (2×)] | |||
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08:34 (cur | prev) +6 Prime.mover talk contribs | |||
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N 08:34 | Acnode/Examples/y^2 = x^3 - x^2 4 changes history +784 [Prime.mover (4×)] | |||
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08:22 (cur | prev) +12 Prime.mover talk contribs | |||
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08:20 (cur | prev) +734 Prime.mover talk contribs (Created page with "== Examples of Acnodes == <onlyinclude> Consider the locus of the equation: :$y^2 = x^3 - x^2$ :320px This has an acnode at $\tuple {0, 0}$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Acnode|next = Definition:Isolated Singularity|e...") | |||
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08:23 | User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Rank Axioms 3 changes history −609 [Leigh.Samphier (3×)] | |||
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08:23 (cur | prev) −5 Leigh.Samphier talk contribs | ||||
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08:19 (cur | prev) −235 Leigh.Samphier talk contribs | ||||
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| N 08:21 | Category:Examples of Acnodes diffhist +54 Prime.mover talk contribs (Created page with "{{ExampleCategory|def = Acnode}} Category:Acnodes") | ||||
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08:21 | Acnode/Examples 2 changes history +121 [Prime.mover (2×)] | |||
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08:21 (cur | prev) +12 Prime.mover talk contribs | ||||
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07:45 (cur | prev) +109 Prime.mover talk contribs | ||||
| 08:20 | Definition:Acnode diffhist +438 Prime.mover talk contribs | ||||
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08:17 | Definition:Isolated Singularity 2 changes history +473 [Prime.mover (2×)] | |||
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| 08:06 | Picard's Existence Theorem/Also known as diffhist +12 Prime.mover talk contribs | ||||
| 07:44 | Upload log Prime.mover talk contribs uploaded File:Y-sq-is-x-cu-minus-x-sq.png | ||||
| 07:32 | Definition:Acnode/Also known as diffhist +404 Prime.mover talk contribs | ||||
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N 07:29 | Definition:Isolation of Root 2 changes history +1,117 [Prime.mover (2×)] | |||
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07:27 (cur | prev) +1,117 Prime.mover talk contribs (Created page with "== Definition == <onlyinclude> Let $\EE$ be an equation which is dependent upon a real variable $x$. '''Isolation''' of a root $x$ of $\EE$ is the process of finding two numbers between which $x$ lies. </onlyinclude> == Also see == {{Link-to-category|Isolation of Roots|isolation of roots}} == Sources =...") | |||
| N 07:28 | Category:Isolation of Roots diffhist +119 Prime.mover talk contribs (Created page with "{{SubjectCategory|Isolation of Root}} Category:Roots of Equations Category:Roots Category:Proof Techniques") | ||||
| N 07:27 | Category:Definitions/Isolation of Roots diffhist +88 Prime.mover talk contribs (Created page with "{{DefinitionCategory|def = Isolation of Root|Roots of Equations|Roots|Proof Techniques}}") | ||||
| m 07:09 | Help:Contents diffhist 0 Prime.mover talk contribs | ||||
| m 07:07 | Definition:Isogonal Polyhedron diffhist +30 Prime.mover talk contribs | ||||
| Nm 07:07 | User talk:Wikimiki diffhist +1,240 Prime.mover talk contribs (Welcome!) | ||||
| Nm 07:07 | User:Wikimiki diffhist +46 Prime.mover talk contribs (Creating user page for new user.) | ||||
24 April 2024
| m 23:54 | 8436 diffhist 0 Prime.mover talk contribs | ||||
| 23:53 | Product of Affine Spaces is Affine Space diffhist +73 Prime.mover talk contribs | ||||
| m 23:49 | Definition:Abhenry/Linguistic Note diffhist +23 Prime.mover talk contribs | ||||
| m 23:48 | Definition:Abhenry diffhist +23 Prime.mover talk contribs | ||||
| m 23:47 | Definition:Inductance diffhist +17 Prime.mover talk contribs | ||||
| m 11:52 | Definition:Inequality/Member diffhist +36 Prime.mover talk contribs | ||||
| m 11:51 | Definition:Inequality/Weak diffhist +36 Prime.mover talk contribs | ||||
| 11:51 | Definition:Inequality/Strict diffhist +34 Prime.mover talk contribs | ||||
| m 11:48 | Definition:Inductance/Unit diffhist +1 Prime.mover talk contribs | ||||
| 10:48 | Category:Isogonal Polyhedra diffhist −5 Prime.mover talk contribs | ||||