Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 2778
- Definitions 2634
- Statements 1926
- Conjectures 38
- Problems 54
- Examples 213
- Counterexamples 52
- Objects 99
- Proofs 10
- Computations 1
- Topics 1
Ideas 751–900 of 1926.
| Name | Kind | Subject |
|---|---|---|
| Triangle inequality for integrals | Theorem | Real functions |
| Composition of continuous functions is continuous | Proposition | Real functions |
| Connected components are closed | Proposition | General topology |
| Characteristic function of the normal distribution | Proposition | Probability theory and stochastic processes |
| Derivative of a map into R^n by components | Proposition | Real functions |
| Discrete Grönwall inequality | Lemma | Real functions |
| Exterior angle theorem | Theorem | Geometry |
| Z/pZ is a field for p prime | Theorem | Number theory |
| Multiplicativity of the Legendre symbol | Theorem | Number theory |
| Second Borel–Cantelli lemma | Lemma | Probability theory and stochastic processes |
| Weierstrass M-test | Theorem | Sequences, series, summability |
| Sum of independent normal random variables | Theorem | Probability theory and stochastic processes |
| Theorem on friends and strangers | Theorem | Combinatorics |
| Angle-angle similarity | Theorem | Geometry |
| Classification of isometries of the plane | Theorem | Geometry |
| Second-order Taylor expansion | Corollary | Real functions |
| Negation of a universal statement | Theorem | Mathematical logic and foundations |
| Sine is 2π-periodic | Theorem | Special functions |
| A function with bounded derivative is Lipschitz | Corollary | Real functions |
| Picard–Lindelöf theorem | Theorem | Ordinary differential equations |
| Compactness via open covers | Proposition | General topology |
| Linearity of expectation | Theorem | Probability theory and stochastic processes |
| Vandermonde determinant | Theorem | Linear and multilinear algebra; matrix theory |
| The exponential function is positive | Proposition | Special functions |
| Metric spaces are Hausdorff | Proposition | General topology |
| Existence of a complementary subspace | Theorem | Linear and multilinear algebra; matrix theory |
| Continuity is equivalent to sequential continuity | Theorem | Real functions |
| Law of sines | Theorem | Geometry |
| Order of the symmetric group | Proposition | Group theory and generalizations |
| Fermat's theorem on stationary points | Theorem | Real functions |
| First supplement to quadratic reciprocity | Theorem | Number theory |
| Heine–Borel theorem in finite-dimensional normed spaces | Theorem | Functional analysis |
| Alternating series test | Theorem | Sequences, series, summability |
| Projections are continuous | Proposition | General topology |
| Order of an inverse | Proposition | Group theory and generalizations |
| The continued fraction of a rational number terminates | Theorem | Number theory |
| The Gaussian integers are a Euclidean domain | Theorem | Number theory |
| Argument principle | Theorem | Functions of a complex variable |
| The constructible numbers form a field closed under square roots | Theorem | Field theory and polynomials |
| Jordan's lemma | Lemma | Functions of a complex variable |
| Interior is open | Proposition | General topology |
| Determinant is multilinear in the rows | Proposition | Linear and multilinear algebra; matrix theory |
| Second isomorphism theorem | Theorem | Group theory and generalizations |
| Probability of the complement | Proposition | Probability theory and stochastic processes |
| Alternating sum of binomial coefficients | Theorem | Combinatorics |
| Principal axis theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Dirichlet convolution of multiplicative functions is multiplicative | Theorem | Number theory |
| Expectation with respect to the binomial distribution | Proposition | Probability theory and stochastic processes |
| The exponential series has infinite radius of convergence | Proposition | Functions of a complex variable |
| Orthogonal complement of the orthogonal complement | Proposition | Functional analysis |
| Stolz–Cesàro theorem | Theorem | Sequences, series, summability |
| Integral of a power | Proposition | Real functions |
| Darboux's theorem | Theorem | Real functions |
| Holomorphic functions with nonzero derivative are conformal | Proposition | Functions of a complex variable |
| Third Sylow theorem | Theorem | Group theory and generalizations |
| Reciprocal rule | Proposition | Real functions |
| Holomorphic functions are infinitely differentiable | Corollary | Functions of a complex variable |
| Cayley–Hamilton theorem for linear maps | Theorem | Linear and multilinear algebra; matrix theory |
| Eigenvalues are the roots of the minimal polynomial | Theorem | Linear and multilinear algebra; matrix theory |
| The algebraic numbers form a field | Theorem | Number theory |
| Gauss's lemma | Theorem | Commutative algebra |
| Irrationality of pi | Theorem | Number theory |
| Dimension of the coordinate space | Proposition | Linear and multilinear algebra; matrix theory |
| Euclidean domains are principal ideal domains | Theorem | Commutative algebra |
| The Galois group has order at most the degree | Theorem | Field theory and polynomials |
| Ratio test | Theorem | Sequences, series, summability |
| Von Dyck's theorem | Theorem | Group theory and generalizations |
| Derivative of a map into a product | Proposition | Real functions |
| Number of odd-degree vertices is even | Corollary | Combinatorics |
| In a UFD irreducible elements are prime | Theorem | Commutative algebra |
| Recurrence for derangements | Theorem | Combinatorics |
| The reals form an ordered field | Theorem | Field theory and polynomials |
| The group of units of Z/pZ is cyclic | Theorem | Number theory |
| Frattini argument | Lemma | Group theory and generalizations |
| Dimension of a subspace | Proposition | Linear and multilinear algebra; matrix theory |
| Every element of a finite field of order q satisfies x^q = x | Proposition | Field theory and polynomials |
| Tangent–secant theorem | Theorem | Geometry |
| Convergent sequences are Cauchy | Proposition | Sequences, series, summability |
| Continuity of the sum of a uniformly convergent series of functions | Corollary | Sequences, series, summability |
| Fubini's theorem | Theorem | Real functions |
| Abelian groups are solvable | Proposition | Group theory and generalizations |
| Fraction in lowest terms | Theorem | Number theory |
| Universal property of the quotient ring | Theorem | Associative rings and algebras |
| Compact subsets of a metric space are bounded | Proposition | General topology |
| Symmetry of binomial coefficients | Theorem | Combinatorics |
| pi is greater than 3 | Proposition | Number theory |
| A linear isometry preserves the inner product | Proposition | Linear and multilinear algebra; matrix theory |
| Dimension of a tensor product | Corollary | Linear and multilinear algebra; matrix theory |
| A linear map is determined by its values on a basis | Proposition | Linear and multilinear algebra; matrix theory |
| Integers modulo a prime form a field | Theorem | Number theory |
| Characterization of the floor | Proposition | Real functions |
| Divisibility by 3 | Proposition | Number theory |
| Gcd of Fibonacci numbers | Theorem | Number theory |
| Limit of a sum of sequences | Proposition | Sequences, series, summability |
| Bessel's inequality | Theorem | Functional analysis |
| Cesàro means of a convergent sequence converge | Proposition | Sequences, series, summability |
| Generating function of a sum of independent random variables | Proposition | Probability theory and stochastic processes |
| Cauchy–Schwarz inequality | Theorem | Linear and multilinear algebra; matrix theory |
| Limit of the cumulative distribution function at infinity | Proposition | Probability theory and stochastic processes |
| Logarithm is the inverse of the exponential | Theorem | Special functions |
| Cantor set is homeomorphic to the space of binary sequences | Theorem | General topology |
| Wedderburn's little theorem | Theorem | Field theory and polynomials |
| Jensen's inequality | Theorem | Real functions |
| Every infinite set has a countably infinite subset | Theorem | Mathematical logic and foundations |
| Image of an intersection | Proposition | Mathematical logic and foundations |
| Distributivity of matrix multiplication | Proposition | Linear and multilinear algebra; matrix theory |
| Chain rule | Theorem | Real functions |
| Structure theorem for finitely generated abelian groups | Theorem | Group theory and generalizations |
| Lucas's theorem | Theorem | Number theory |
| Law of excluded middle | Theorem | Mathematical logic and foundations |
| A nontrivial finite p-group has nontrivial centre | Theorem | Group theory and generalizations |
| Power-reduction formula for cosine | Corollary | Special functions |
| Size of an orbit times the size of the stabiliser | Corollary | Group theory and generalizations |
| Variation of constants formula for linear systems | Theorem | Ordinary differential equations |
| Abel's theorem | Theorem | Sequences, series, summability |
| Convergent sequences are bounded | Proposition | Sequences, series, summability |
| Inverse of a product | Proposition | Linear and multilinear algebra; matrix theory |
| Order of the group of units of Z/nZ is Euler's totient | Proposition | Number theory |
| Hartman–Grobman theorem | Theorem | Dynamical systems and ergodic theory |
| Correspondence theorem | Theorem | Group theory and generalizations |
| Derivative of tangent | Proposition | Special functions |
| Dirichlet convolution formula | Proposition | Number theory |
| Gradient theorem | Theorem | Real functions |
| Product rule in several variables | Proposition | Real functions |
| Basis of a tensor product | Theorem | Linear and multilinear algebra; matrix theory |
| Closure is the smallest closed superset | Proposition | General topology |
| Irreducibility of the cyclotomic polynomials over the rationals | Theorem | Number theory |
| Stability of linear systems via eigenvalues | Theorem | Ordinary differential equations |
| Edge bound for planar graphs | Theorem | Combinatorics |
| Erdős–Szekeres theorem | Theorem | Combinatorics |
| A space is the direct sum of a subspace and its orthogonal complement | Theorem | Functional analysis |
| Existence of a prime divisor | Proposition | Number theory |
| Change of basis for a bilinear form | Proposition | Linear and multilinear algebra; matrix theory |
| The Gaussian integers form a Euclidean domain | Theorem | Number theory |
| Principal value of the argument | Proposition | Functions of a complex variable |
| Subgroups of the integers | Proposition | Group theory and generalizations |
| Characteristic subgroups are normal | Proposition | Group theory and generalizations |
| Hurwitz's theorem | Theorem | Functions of a complex variable |
| The degree of a constructible number is a power of two | Theorem | Field theory and polynomials |
| Moments are derivatives of the moment-generating function at zero | Theorem | Probability theory and stochastic processes |
| C^1 functions are strictly differentiable | Proposition | Real functions |
| Density of the rationals | Theorem | Real functions |
| Almost sure convergence implies convergence in probability | Theorem | Probability theory and stochastic processes |
| Primitive element theorem | Theorem | Field theory and polynomials |
| Möbius transformations map circles and lines to circles and lines | Theorem | Functions of a complex variable |
| Dimension of a quotient space | Proposition | Linear and multilinear algebra; matrix theory |
| Order of the alternating group | Proposition | Group theory and generalizations |
| Determinant is a coefficient of the characteristic polynomial | Proposition | Linear and multilinear algebra; matrix theory |
| Infinitely many primes congruent to 1 modulo n | Theorem | Number theory |
| Fundamental theorem of Galois theory | Theorem | Field theory and polynomials |