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- 02:13, 25 May 2012 Nth Derivative of Nth Power (hist) [911 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Nth Derivative of Mth Power == Let $n \in \Z$ be an integer such that $n \ge 0$. The [[Definition:Derivative/Higher Derivatives|$n...")
- 17:56, 24 May 2012 Union of Relative Complements (hist) [1,282 bytes] Lord Farin (Talk | contribs) (Created page with "== Theorem == Let $R \subseteq S \subseteq T$ be sets with the indicated inclusions. Then: :$\complement_T \left({S}\right) \cup \...")
- 17:06, 24 May 2012 Set Union Preserves Subsets/Corollary (hist) [562 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Set Union Preserves Subsets == <onlyinclude> Let $A, B, S$ be sets. Then: :$A \subseteq B \implies A \cup S \subseteq B \cup S$ </onlyi...")
- 02:18, 24 May 2012 Intersection Subset/General Result (hist) [708 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $S$ be a set. Let $\mathcal P \left({S}\right)$ be the power set of $S$. Let $\mathbb S \subseteq...")
- 02:10, 24 May 2012 Union with Empty Set/Proof 2 (hist) [431 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The union of any set with the empty set is the set itself: :$S \cup \varnothing = S$ == ...")
- 02:09, 24 May 2012 Union with Empty Set/Proof 1 (hist) [838 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The union of any set with the empty set is the set itself: :$S \cup \varnothing = S$ == ...")
- 18:09, 23 May 2012 Union is Empty iff Sets are Empty/Proof 2 (hist) [785 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == If the union of two sets is the empty set, then both are themselves [[Definition:Empty Set|...")
- 18:08, 23 May 2012 Union is Empty iff Sets are Empty/Proof 1 (hist) [1,068 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == If the union of two sets is the empty set, then both are themselves [[Definition:Empty Set|...")
- 16:44, 23 May 2012 Trace Sigma-Algebra of Generated Sigma-Algebra (hist) [3,284 bytes] Lord Farin (Talk | contribs) (Created page with "== Theorem == Let $X$ be a Set, and let $\mathcal G \subseteq \mathcal P \left({X}\right)$ be a collection of subsets of $X$. Let $A...")
- 18:10, 22 May 2012 Linear Combination of Sequence is Linear Combination of Set (hist) [2,966 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be an $R$-module. Let $\left \langle {a_k} \right \rangle_{1 \mathop \le k \mathop \le n}$ be a [[Definition:Sequence|sequence of...")
- 16:06, 22 May 2012 Sigma-Algebra is Monotone Class (hist) [767 bytes] Lord Farin (Talk | contribs) (Created page with "== Theorem == Let $\Sigma$ be a $\sigma$-algebra on a set $X$. Then $\Sigma$ is also a [[Definition:Monotone Class|monotone ...")
- 15:32, 22 May 2012 Intersection and Sum of Submodules/Corollary (hist) [974 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Intersection and Sum of Submodules == <onlyinclude> Let $\left({G, +, \circ}\right)_R$ be an $R$-module. [[Definition:Ordering|Order...")
- 03:32, 22 May 2012 Condition on Equality of Generated Sigma-Algebras (hist) [1,060 bytes] Lord Farin (Talk | contribs) (Created page with "== Theorem == Let $X$ be a set, and let $\mathcal G$, $\mathcal H$ be collections of subsets of $X$. Supp...")
- 03:25, 22 May 2012 Generated Sigma-Algebra by Generated Monotone Class/Corollary (hist) [1,802 bytes] Lord Farin (Talk | contribs) (Created page with "== Corollary to Generated Sigma-Algebra by Generated Monotone Class == Let $X$ be a set, and let $\mathcal G \subseteq \mathcal P \left({X}\right)$ be ...")
- 16:43, 21 May 2012 Submodule of Module of Polynomial Functions (hist) [899 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $K$ be a commutative ring with unity. Let $P \left({K}\right)$ be the set of all [[Definition:Polynomial Functi...")
- 02:12, 21 May 2012 Subspaces of Dimension 2 Real Vector Space/Proof 2 (hist) [511 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Take the $\R$-vector space $\left({\R^2, +, \times}\right)_\R$. Let $S$ be a subspace of $\left...")
- 02:11, 21 May 2012 Subspaces of Dimension 2 Real Vector Space/Proof 1 (hist) [2,212 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Take the $\R$-vector space $\left({\R^2, +, \times}\right)_\R$. Let $S$ be a subspace of $\left...")
- 01:22, 21 May 2012 Null Module is Module (hist) [605 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({R, +_R, \circ_R}\right)$ be a ring. Let $G$ be the trivial group. Let $\left(...")
- 14:29, 20 May 2012 Trivial Module is Not Unitary (hist) [1,414 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e_G$. Let $\left({R, +_R, \circ...")
- 14:27, 20 May 2012 Trivial Module is Module (hist) [1,262 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e_G$. Let $\left({R, +_R, \circ...")
- 13:09, 20 May 2012 Subring Module/Special Case (hist) [840 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $S$ be a subring of the ring $\left({R, +, \circ}\right)$. <onlyinclude> Let $\circ$ be the [...")
- 09:29, 20 May 2012 Zero Vector Space Product iff Factor is Zero/Proof 2 (hist) [888 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, \circ}\right)$ be a group whose identity is $e$. Let $\left({K, +, \circ}\right)$ be a [[De...")
- 09:28, 20 May 2012 Zero Vector Space Product iff Factor is Zero/Proof 1 (hist) [1,431 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, \circ}\right)$ be a group whose identity is $e$. Let $\left({K, +, \circ}\right)$ be a [[De...")
- 09:22, 20 May 2012 Scalar Product with Multiple of Unity (hist) [1,050 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e$. Let $\left({R, +_R, \times_...")
- 09:18, 20 May 2012 Scalar Product with Inverse Unity (hist) [900 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $\left({G, +_G}\right)$ be an abelian group whose identity is $e$. Let $\left({R, +_R, \times_...")
- 07:24, 19 May 2012 Sigma-Algebra Extended by Single Set (hist) [4,824 bytes] Lord Farin (Talk | contribs) (Created page with "== Theorem == Let $\Sigma$ be a $\sigma$-algebra on a set $X$. Let $S \subseteq X$ be a subset of $X$. For [[Definition:...")
- 06:11, 19 May 2012 Cauchy-Hadamard Theorem (hist) [2,469 bytes] Corifeo (Talk | contribs) (Created page with "Cauchy Hadamard Theorem")
- 04:22, 19 May 2012 Conjugacy Class Equation/Proof 2 (hist) [1,509 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be a group. Let $\left|{G}\right|$ be the order of $G$. Let $Z \left({G}\right)$ be the [[Def...")
- 04:19, 19 May 2012 Conjugacy Class Equation/Proof 1 (hist) [2,540 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be a group. Let $\left|{G}\right|$ be the order of $G$. Let $Z \left({G}\right)$ be the [[Def...")
- 04:04, 19 May 2012 Center is a Subgroup/Proof 1 (hist) [1,977 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The center $Z \left({G}\right)$ of any group $G$ is a subgroup of $G$. == Proof ==...")
- 04:04, 19 May 2012 Center is a Subgroup/Proof 2 (hist) [850 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The center $Z \left({G}\right)$ of any group $G$ is a subgroup of $G$. == Proof ==...")
- 14:41, 18 May 2012 Conjugacy Classes of Center Elements are Singletons/Corollary (hist) [867 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Conjugacy Classes of Center Elements are Singletons == Let $G$ be a group. Let $Z \left({G}\right)$ be the [[Definition:Center of Gr...")
- 14:29, 18 May 2012 Odd Order Group Element is a Square/Corollary (hist) [1,409 bytes] Prime.mover (Talk | contribs) (Created page with "=== Corollary to Odd Order Group Element is a Square === <onlyinclude> Let $\left({G, \circ}\right)$ be a group whose [[Definition:Identity Element|id...")
- 13:50, 18 May 2012 Fermat's Little Theorem/Corollary 1/Proof 2 (hist) [2,101 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Fermat's Little Theorem == If $p$ is a prime number, then $n^p \equiv n \pmod p$. == Proof == <onlyinclude> Suppose we want ...")
- 13:49, 18 May 2012 Fermat's Little Theorem/Corollary 1/Proof 1 (hist) [542 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Fermat's Little Theorem == If $p$ is a prime number, then $n^p \equiv n \pmod p$. == Proof == <onlyinclude> There are two ca...")
- 01:21, 18 May 2012 Fermat's Little Theorem/Proof 3 (hist) [596 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == If $p$ is a prime number and $p \nmid n$, then $n^{p-1} \equiv 1 \pmod p$. == Proof == <onlyinclude> From [[Multiplicative Group o...")
- 01:18, 18 May 2012 Fermat's Little Theorem/Proof 2 (hist) [668 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == If $p$ is a prime number and $p \nmid n$, then $n^{p-1} \equiv 1 \pmod p$. == Proof == <onlyinclude> By [[Prime Not Divisor then C...")
- 01:17, 18 May 2012 Fermat's Little Theorem/Proof 1 (hist) [1,595 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == If $p$ is a prime number and $p \nmid n$, then $n^{p-1} \equiv 1 \pmod p$. == Proof == <onlyinclude> Consider the sequence of inte...")
- 01:15, 18 May 2012 Fermat's Little Theorem/Corollary 2 (hist) [793 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Fermat's Little Theorem == <onlyinclude> If $p$ is a prime number, then: :$n^{p-1} \equiv \left[{p \nmid n}\right] \pmod p$ whe...")
- 01:12, 18 May 2012 Fermat's Little Theorem/Corollary 1 (hist) [964 bytes] Prime.mover (Talk | contribs) (Created page with "== Corollary to Fermat's Little Theorem == <onlyinclude> If $p$ is a prime number, then $n^p \equiv n \pmod p$. </onlyinclude> == Proof == T...")
- 01:25, 17 May 2012 Ring of Integers is Principal Ideal Domain/Proof 2 (hist) [358 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The integers $\Z$ form a principal ideal domain. == Proof == <onlyinclude> We have that [[Integer...")
- 01:24, 17 May 2012 Ring of Integers is Principal Ideal Domain/Proof 1 (hist) [853 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == The integers $\Z$ form a principal ideal domain. == Proof == <onlyinclude> Let $J$ be an [[Defini...")
- 18:57, 16 May 2012 Primary Decomposition Theorem (hist) [10,173 bytes] Frades (Talk | contribs) (Created page with "== Theorem == Let $T:V \to V$ be a linear application on some vector space $V$ over some field $K$ and let $p(x) \in K[x]$ be a polynomial such that $p(T)=0$. By [[Polynomial...")
- 16:55, 16 May 2012 Subgroup of Cyclic Group is Cyclic/Proof 2 (hist) [1,864 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == A subgroup of a cyclic group is cyclic. == Proof == <onlyinclude> Let $G$ be a cyclic group [[Definition:G...")
- 16:54, 16 May 2012 Subgroup of Cyclic Group is Cyclic/Proof 1 (hist) [2,068 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == A subgroup of a cyclic group is cyclic. == Proof == <onlyinclude> Let $G$ be a cyclic group [[Definition:G...")
- 01:21, 16 May 2012 Cosets are Equivalent/Proof 2 (hist) [863 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == All left cosets of a group $G$ with respect to a subgroup $H$ are [[Definition:Set Equiva...")
- 01:17, 16 May 2012 Cosets are Equivalent/Proof 1 (hist) [1,734 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == All left cosets of a group $G$ with respect to a subgroup $H$ are [[Definition:Set Equiva...")
- 02:28, 15 May 2012 Lagrange's Theorem (Group Theory)/Proof 3 (hist) [1,476 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be a group of finite order. Let $H$ be a [[Definition:Subgroup|subgroup]...")
- 02:27, 15 May 2012 Lagrange's Theorem (Group Theory)/Proof 2 (hist) [3,022 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be a group of finite order. Let $H$ be a [[Definition:Subgroup|subgroup]...")
- 02:25, 15 May 2012 Lagrange's Theorem (Group Theory)/Proof 1 (hist) [1,932 bytes] Prime.mover (Talk | contribs) (Created page with "== Theorem == Let $G$ be a group of finite order. Let $H$ be a [[Definition:Subgroup|subgroup]...")
