مستخدم:Chaos/قائمة البراهين الرياضية

من ويكيبيديا، الموسوعة الحرة

A list of articles with mathematical proofs:

فهرست

[تحرير] Theorems of which articles are primarily devoted to proving them

  • Bertrand's postulate and a proof
  • Estimation of covariance matrices
  • Fermat's little theorem and some proofs
  • Gödel's completeness theorem and its original proof
  • Mathematical induction and a proof
  • Proof that 0.999... equals 1
  • Proof that 22/7 exceeds π
  • Proof that e is irrational
  • Proof that the sum of the reciprocals of the primes diverges

[تحرير] Articles devoted to theorems of which a (sketch of a) proof is given

  • Banach fixed point theorem
  • Banach–Tarski paradox
  • Basel problem
  • Bolzano-Weierstrass theorem
  • Brouwer fixed point theorem
  • Buckingham π theorem (proof in progress)
  • Burnside's lemma
  • Cantor's theorem
  • Cantor–Bernstein–Schroeder theorem
  • Cayley's formula
  • Cayley's theorem
  • Clique problem (to do)
  • Compactness theorem (very compact proof)
  • Erdős-Ko-Rado theorem
  • Euler's formula
  • Euler's four-square identity
  • Euler's theorem
  • Five color theorem
  • Five lemma
  • Fundamental theorem of arithmetic
  • Gauss-Markov theorem (brief pointer to proof)
  • Gödel's incompleteness theorem
    • Gödel's first incompleteness theorem
    • Gödel's second incompleteness theorem
  • Goodstein's theorem
  • Green's theorem (to do)
    • Green's theorem when D is a simple region
  • Heine-Borel theorem
  • Intermediate value theorem
  • Itô's lemma
  • König's lemma
  • König's theorem (to do)
  • Lagrange's theorem
  • Liouville's theorem (brief pointer to proof)
  • Markov's inequality (proof of a generalization)
  • Mean value theorem
  • Multivariate normal distribution (to do)
  • Holomorphic functions are analytic
  • Pythagorean theorem
  • Quadratic equation
  • Quotient rule
  • Ramsey's theorem
  • Rao-Blackwell theorem
  • Rice's theorem
  • Rolle's theorem
  • Splitting lemma
  • squeeze theorem
  • Sum rule in differentiation
  • Sum rule in integration
  • Sylow theorem
  • Transcendence of e and π (as corollaries of Lindemann-Weierstrass)
  • Tychonoff's theorem (to do)
  • Ultrafilter lemma
  • Ultraparallel theorem
  • Urysohn's lemma
  • Van der Waerden's theorem
  • Wilson's theorem
  • Zorn's lemma

[تحرير] Articles devoted to algorithms in which their correctness is proven

  • Bellman-Ford algorithm (to do)
  • Euclidean algorithm
  • Kruskal's algorithm
  • Prim's algorithm
  • Shor's algorithm (incomplete)

[تحرير] Articles where example statements are proven

  • Basis (linear algebra)
  • Burrows-Abadi-Needham logic
  • Generating a vector space
  • Linear independence
  • Polynomial
  • Proof
  • Pumping lemma
  • Simpson's rule

[تحرير] Other articles containing proofs

  • Addition in N
    • associativity of addition in N
    • commutativity of addition in N
    • uniqueness of addition in N
  • Algorithmic information theory
  • Boolean ring
    • commutativity of a boolean ring
  • Boolean satisfiability problem
    • NP-completeness of the Boolean satisfiability problem
  • Calculus with polynomials
  • Cantor's diagonal argument
    • set is smaller than its power set
    • uncountability of the real numbers
  • Combinatorics
  • Combinatory logic
  • Co-NP
  • Coset
  • Countable
    • countability of a subset of a countable set (to do)
  • Counter
  • Angle of parallelism
  • Galois group
    • Fundamental theorem of Galois theory (to do)
  • Gödel number
    • Gödel's incompleteness theorem
  • Group (mathematics)
  • Halting problem
    • insolubility of the halting problem
  • Harmonic series (mathematics)
    • divergence of the (standard) harmonic series
  • Highly composite number
  • Area of hyperbolic sector, basis of hyperbolic angle
  • Infinite series
    • convergence of the geometric series with first term 1 and ratio 1/2
  • Integer partition
  • Irrational number
    • irrationality of log23
    • irrationality of the square root of 2
  • Limit point
  • Mathematical induction
    • sum identity
  • Prime number
    • Infinitude of the prime numbers
  • Primitive recursive function
  • Principle of bivalence
    • no propositions are neither true nor false in intuitionistic logic
  • Recursion
  • Relational algebra (to do)
  • Solvable group
  • Square root of 2
  • Tetris
  • Algebra of sets
    • idempotent laws for set union and intersection

[تحرير] Articles which mention dependencies of theorems

  • Cauchy's integral formula
  • Cauchy integral theorem
  • Computational geometry
  • Fundamental theorem of algebra
  • Lambda calculus
  • Invariance of domain
  • Minkowski inequality
  • Nash embedding theorem
  • Open mapping theorem
  • Product topology
  • Riemann integral
  • Time hierarchy theorem
    • Deterministic time hierarchy theorem

[تحرير] Articles giving mathematical proofs within a physical model

  • No cloning theorem
  • Proof of angular momentum

[تحرير] Other related articles

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