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References to 'necessary and sufficient'
1. $C$-embedding by CWoo
2. $e^r$ is irrational for $r\in\mathbb{Q}\setminus\{0\}$ by Cosmin
3. $GL_2(\mathbb{Z})$ by rm50
4. $x^4-y^4=z^2$ has no solutions in positive integers by rm50
5. $Z_2$ by Henry
6. $\ell$-adic \'etale cohomology by mathcam
7. a compact metric space is second countable by azdbacks4234
8. a demonstration of different encryption methods on the same sample message by PrimeFan
9. a sufficient condition for convergence of integral by pahio
10. adjacent fraction by XJamRastafire
11. Albert Einstein by PrimeFan
12. algebraic geometry by archibal
13. algebras by Algeboy
14. algorithm for modular exponentiation by PrimeFan
15. almost everywhere by mathcam
16. alternating series test by Koro
17. alternative proof of necessity direction of equivalent conditions for triangles (hyperbolic and spherical) by Wkbj79
18. amenable number by PrimeFan
19. approximating Fourier integrals with discrete Fourier transforms by stevecheng
20. Aristotelian logic by Daume
21. arithmetic encoding by vampyr
22. arithmetical hierarchy by CWoo
23. axiom of choice by GrafZahl
24. base conversion by mathcam
25. Beurling-Ahlfors quasiconformal extension by jirka
26. beyond formalism: G\"{o}del's incompleteness by gribskoff
27. bilinear form by rmilson
28. Boolean algebra homomorphism by CWoo
29. Boolean subalgebra by CWoo
30. bounded linear functionals on $L^\infty(\mu)$ by gel
31. Bourbaki, Nicolas by Daume
32. Brauer's ovals theorem by Andrea Ambrosio
33. cancellative semigroup by yark
34. Cantor-Zassenhaus split by mathwizard
35. categorical quantum logics as quantum LM-algebraic logic by bci1
36. category of automata by bci1
37. Cauchy integral formula by djao
38. Cauchy product by msihl
39. Cayley graph by Mathprof
40. Cayley's parameterization of orthogonal matrices by rspuzio
41. centered hexagonal number by PrimeFan
42. characterisation by pahio
43. circulation and vorticity by perucho
44. classical groups by Algeboy
45. classical ring of quotients by mclase
46. coefficients of Laurent series by pahio
47. colorings of plane graphs by marijke
48. combinatorial proof of Zeckendorf's theorem by rm50
49. combining URMs by CWoo
50. compass and straightedge construction of parallel line by pahio
51. complete category by CWoo
52. complete ultrametric field by pahio
53. completion by djao
54. composition algebra by Algeboy
55. composition algebras over $\mathbb{Q}$ by Algeboy
56. composition series by mclase
57. connection by rspuzio
58. construction of polar coordinates by CWoo
59. construction of well-formed formulas by CWoo
60. continuous functions on the extended real numbers by Wkbj79
61. converse by pahio
62. counter example to Nakayama's lemma for non-finitely generated modules by sjm
63. counter-example of Fubini's theorem for the Lebesgue integral by rmilson
64. counter-example to Tonelli's theorem by rmilson
65. covering system by PrimeFan
66. Coxeter group by Simone
67. criterion for constructibility of regular polygon by Wkbj79
68. criterion of N\'eron-Ogg-Shafarevich by alozano
69. criterion of surjectivity by pahio
70. cyclic quadrilateral by drini
71. de Polignac's formula by PrimeFan
72. decimal expansion by pahio
73. defect theorem by Ziosilvio
74. derivative of homogeneous function by matte
75. derivatives by pure algebra by Algeboy
76. derived functor by mathcam
77. determining rank of matrix by Algeboy
78. determining the continuations of exponent by pahio
79. diagonalization by rmilson
80. diamond lemma by CWoo
81. differentiable function by Koro
82. differential geometry by rspuzio
83. differentiation under the integral sign by stevecheng
84. division algebra by Algeboy
85. Doob's optional sampling theorem by skubeedooo
86. dual of Dilworth's theorem by justice
87. Dyck language by CWoo
88. economic context of Egyptian fractions by milogardner
89. eigenvalue problem by archibal
90. Einstein summation convention by PrimeFan
91. equitable matrices of order $2$ by matte
92. equivalent conditions for triangles by Wkbj79
93. Euler's equation for rigid bodies by perucho
94. Euler-Lagrange differential equation (elementary) by rspuzio
95. every PID is a UFD by rm50
96. example needing two Lagrange multipliers by pahio
97. example of a universal structure by uzeromay
98. example of algebras and coalgebras which cannot be turned into Hopf algebras by joking
99. example of computing limits using Taylor expansion by stevecheng
100. example of exact functor by CWoo
101. example of false implies true by Algeboy
102. example of Lipschitz condition by me_and
103. example of Nash equilibrium by Henry
104. example of Schreier's Lemma by Algeboy
105. examples of logarithms simplifying calculations by PrimeFan
106. examples of symplectic manifolds by mathcam
107. existence of Hilbert class field by mathcam
108. extension and restriction of states by asteroid
109. factorization criterion by CWoo
110. false counterexamples to Fermat's last theorem by PrimeFan
111. Fine and Wilf's theorem on words by Ziosilvio
112. finite field by yark
113. finite projective plane by Mathprof
114. formal grammar by CWoo
115. foundations of mathematics: overview by gribskoff
116. free product with amalgamated subgroup by mathcam
117. from Hilbert's tenth problem to G\"{o}del's trichotomy by gribskoff
118. functional calculus by asteroid
119. fundamental theorem of arithmetic, proof of the by mps
120. fundamental theorem of calculus for Kurzweil-Henstock integral by jirka
121. game theory by Henry
122. general solution of linear differential equation by pahio
123. generalized Boolean algebra by CWoo
124. geometric representation of relation composition by Jon Awbrey
125. geometry by rspuzio
126. Grammian determinant by slider142
127. graph-theoretic representation of relation composition by Jon Awbrey
128. group extension by CWoo
129. groupoid and group representations related to quantum symmetries by bci1
130. G\"odel's incompleteness theorems by mathcam
131. Haar integral by rspuzio
132. Hamiltonian graph by drini
133. happy ending problem by PrimeFan
134. Harnack theorem by perucho
135. Hausdorff metric inherits completeness by mps
136. history of mathematics in the United States of America by PrimeFan
137. homothetic by drini
138. How are normal and T4 spaces defined in books? by Mathprof
139. how to multiply polynomials by Algeboy
140. Hurwitz matrix by lha
141. ideal completion of a poset by CWoo
142. in-place sorting algorithm by archibal
143. incidence geometry by CWoo
144. index of tables by PrimeFan
145. infinite descent by Thomas Heye
146. infinitely-differentiable function that is not analytic by ariels
147. inflection points and canonical forms of non-singular cubic curves by rspuzio
148. integer contraharmonic means by pahio
149. integral representation of the hypergeometric function by rspuzio
150. interval by PrimeFan
151. inverse function by matte
152. isomorphic groups by alozano
153. isotope of a groupoid by CWoo
154. Jones Polynomial by Stephaninos
155. Kleene's theorem by CWoo
156. least prime factor by PrimeFan
157. Lewy extension theorem by jirka
158. limit of real number sequence by pahio
159. line of curvature by pahio
160. linear code by mathcam
161. local martingale by skubeedooo
162. local properties of processes by gel
163. logical axiom by CWoo
164. logical implication by Jon Awbrey
165. lower bound for sorting by stevecheng
166. L\"ob's theorem by dankomed
167. mathematical platonism by gribskoff
168. mathematics vocabulary by matte
169. methods to find extremum by bloftin
170. metric system by PrimeFan
171. modular lattice by yark
172. motion of continuum by perucho
173. motivation for von Neumann ordinals by yark
174. Myhill-Nerode theorem for semigroups by Ziosilvio
175. near operators by mathcam
176. negative number by PrimeFan
177. neutrosophic probability by para0doxa
178. no-arbitrage in the Black-Scholes pricing model by stevecheng
179. non-deterministic finite automaton by mps
180. non-existence of universal series convergence criterion by pahio
181. normal equations by akrowne
182. organismic supercategories and super-complex systems biodynamics by bci1
183. orthogonal polynomials by akrowne
184. partial fractions of expressions and partition problems (recreational) by rspuzio
185. Paul L\'evy continuity theorem by Koro
186. pencil of lines by pahio
187. perfect field by sleske
188. perfect number by Wkbj79
189. pivoting by akrowne
190. point-free geometry by ggerla
191. pointed topological space by bwebste
192. Polish notation by PrimeFan
193. polynomial function is a proper map by joking
194. primality by PrimeFan
195. prime harmonic series by Cosmin
196. primitive element theorem by alozano
197. primitive matrix by Mathprof
198. probabilistic method by bbukh
199. probabilistic proof by Algeboy
200. proof by PrimeFan
201. proof of PTAH inequality by Mathprof
202. proof of $L^p$-norm is dual to $L^q$ by gel
203. proof of 5-lemma by bwebste
204. proof of Bondy and Chv\'atal theorem by taxipom
205. proof of casus irreducibilis for real fields by rm50
206. proof of characterization of perfect fields by mclase
207. proof of Chebyshev's inequality by pbruin
208. proof of functional monotone class theorem by gel
209. proof of Heine-Borel theorem by stevecheng
210. proof of infinite product of sums $1\!+\!a_i$ result without exponentials by rspuzio
211. proof of invariance of dimension by Algeboy
212. proof of necessary and sufficient conditions for a normed vector space to be a Banach space by willny
213. proof of Pythagorean triples by fredlb
214. proof of Rolle's theorem by rmilson
215. proof of Stone-Weierstrass theorem by rspuzio
216. proof of theorem about cyclic subspaces by FunctorSalad
217. proof of Vitali convergence theorem by stevecheng
218. proof of Vizing's theorem (for graphs) by marijke
219. proof of Wagner's theorem by Ziosilvio
220. proof of Wilson's theorem by Cosmin
221. proof that 3 is the only prime perfect totient number by PrimeFan
222. proper divisor by PrimeFan
223. properties of non-archimedean valuations by rm50
224. properties of symmetric difference by CWoo
225. propositional calculus by Jon Awbrey
226. pseudorandom numbers by akrowne
227. quantum category by bci1
228. quicksort by thouis
229. random numbers by akrowne
230. recursive algorithm for factorial function by PrimeFan
231. Red Auxiliary numbers, the first LCM method by milogardner
232. regularity theorem for the Laplace equation by rspuzio
233. relation algebra by CWoo
234. relation reduction by Jon Awbrey
235. relation theory by Jon Awbrey
236. relationship between totatives and divisors by Wkbj79
237. restricted direct product of algebraic systems by CWoo
238. Richard Stanley by PrimeFan
239. scheme by djao
240. Schinzel's Hypothesis H by jtolliver
241. scientific notation by PrimeFan
242. score function by CWoo
243. second fundamental form by stevecheng
244. semilattice by mclase
245. semimartingale by gel
246. separability is required for integral closures to be finitely generated by rm50
247. set by Mathprof
248. set theory by mathwizard
249. sheaf by djao
250. Sheffer stroke by CWoo
251. sign relation by Jon Awbrey
252. simplex algorithm by Mathprof
253. simply transitive by benjaminfjones
254. slope of a line is well-defined, proof that the by Dr_Absentius
255. Smirnov metrization theorem by rm50
256. sole sufficient operator by Jon Awbrey
257. space curve by Mathprof
258. Stephen William Hawking by bci1
259. strict by rspuzio
260. subfield criterion by pahio
261. sufficient statistic by CWoo
262. Sun's conjecture on sums of primes and triangular numbers by PrimeFan
263. supercomputers by bci1
264. surface integration with respect to area by rspuzio
265. table of integer factorizations for $0 < n < 1001$ by PrimeFan
266. tensor by rmilson
267. tensor product and dual spaces by joking
268. the real numbers are indecomposable as a topological space by joking
269. theory for separation of variables by pahio
270. theory from orders of classical groups by Algeboy
271. Thurston's geometrization conjecture by PrimeFan
272. topological ring by djao
273. torsion (space curve) by rmilson
274. trace forms on algebras by Algeboy
275. transversals / lifts / sifts by Algeboy
276. tree traversals by mps
277. triple cross product by pahio
278. Tutte theorem by scineram
279. universal assumption by Wkbj79
280. universal coefficient theorem by mps
281. universe by archibal
282. values of $\displaystyle \sum_{i = 0}^n \frac{1}{i!}$ for $0 < n < 26$ by PrimeFan
283. vector norm by mike
284. vector subspace by yark
285. vibrating string by perucho
286. well-founded recursion by CWoo