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 151–300 of 1926.
| Name | Kind | Subject |
|---|---|---|
| log x is at most x - 1 | Proposition | Special functions |
| Determinant is multiplicative | Theorem | Linear and multilinear algebra; matrix theory |
| Spectral theorem for normal matrices | Theorem | Linear and multilinear algebra; matrix theory |
| Variance under translation | Proposition | Probability theory and stochastic processes |
| Order of a group is the index times the order of the subgroup | Theorem | Group theory and generalizations |
| Uniqueness of the supremum | Proposition | Order, lattices, ordered algebraic structures |
| Riesz representation theorem in finite dimensions | Theorem | Functional analysis |
| Density of the irrationals | Theorem | Real functions |
| Dirichlet's approximation theorem | Theorem | Number theory |
| Hockey-stick identity | Theorem | Combinatorics |
| Sum of two squares theorem | Theorem | Number theory |
| Euler's formula | Theorem | Special functions |
| Cyclic groups are abelian | Proposition | Group theory and generalizations |
| Law of total expectation | Theorem | Probability theory and stochastic processes |
| Zorn's lemma | Theorem | Mathematical logic and foundations |
| Chinese remainder theorem for non-coprime moduli | Theorem | Number theory |
| Contrapositive | Theorem | Mathematical logic and foundations |
| Multiplicativity of the divisor function | Theorem | Number theory |
| Integral of cosine | Proposition | Real functions |
| Existence of primitive roots modulo a prime | Theorem | Number theory |
| Every connected graph has a spanning tree | Theorem | Combinatorics |
| Monotone functions are Riemann integrable | Theorem | Real functions |
| Comparison test | Theorem | Sequences, series, summability |
| The real numbers are uncountable | Theorem | Mathematical logic and foundations |
| Euclid's lemma | Lemma | Number theory |
| Product of a matrix and its adjugate | Theorem | Linear and multilinear algebra; matrix theory |
| Eigenvalues are the roots of the characteristic polynomial | Theorem | Linear and multilinear algebra; matrix theory |
| Compact iff complete and totally bounded | Theorem | General topology |
| Fermat numbers are pairwise coprime | Theorem | Number theory |
| PID implies UFD | Theorem | Commutative algebra |
| Lebesgue's criterion for Riemann integrability | Theorem | Real functions |
| A matrix is diagonalisable iff it has a basis of eigenvectors | Theorem | Linear and multilinear algebra; matrix theory |
| Isosceles triangle theorem | Theorem | Geometry |
| Generating function for partitions | Theorem | Number theory |
| The nth roots of unity | Theorem | Number theory |
| Number of compositions | Theorem | Combinatorics |
| Ptolemy's theorem | Theorem | Geometry |
| Scalar triple product | Proposition | Linear and multilinear algebra; matrix theory |
| Isomorphism with the coordinate space | Proposition | Linear and multilinear algebra; matrix theory |
| Sum of a finite geometric series | Proposition | Sequences, series, summability |
| Expectation of a product of independent random variables | Theorem | Probability theory and stochastic processes |
| Stabilisers of points in the same orbit are conjugate | Proposition | Group theory and generalizations |
| Zeckendorf's theorem | Theorem | Number theory |
| Polarisation identity | Proposition | Functional analysis |
| Root test | Theorem | Sequences, series, summability |
| Inner automorphism group is isomorphic to G modulo its centre | Theorem | Group theory and generalizations |
| Poincaré lemma for one-forms on convex sets | Theorem | Global analysis, analysis on manifolds |
| Angle sum of a triangle | Theorem | Geometry |
| Groups of prime order are cyclic | Corollary | Group theory and generalizations |
| Subgroup criterion | Proposition | Group theory and generalizations |
| Composition of continuous maps is continuous | Proposition | General topology |
| Derivative of arctangent | Proposition | Special functions |
| Markov's inequality | Theorem | Probability theory and stochastic processes |
| Matrix of a composition is the product of matrices | Theorem | Linear and multilinear algebra; matrix theory |
| Additivity of the integral over intervals | Theorem | Real functions |
| Laplacian as a sum of second partial derivatives | Proposition | Partial differential equations |
| Number of edges of a complete graph | Proposition | Combinatorics |
| Harmonic numbers grow like log n | Theorem | Number theory |
| Negation of an existential statement | Theorem | Mathematical logic and foundations |
| Equality of complex numbers | Proposition | Functions of a complex variable |
| Maximal ideals are prime | Corollary | Commutative algebra |
| Jacobian of spherical coordinates | Proposition | Real functions |
| Subgroups of solvable groups are solvable | Proposition | Group theory and generalizations |
| Law of cosines | Theorem | Geometry |
| Lucas–Lehmer test | Theorem | Number theory |
| First fundamental theorem of calculus | Theorem | Real functions |
| LaSalle's invariance principle | Theorem | Ordinary differential equations |
| Inclusion of a subspace is continuous | Proposition | General topology |
| Repeating decimals are rational | Theorem | Number theory |
| De Moivre–Laplace theorem | Theorem | Probability theory and stochastic processes |
| Closed subsets of compact sets are compact | Proposition | General topology |
| The integers are countable | Proposition | Mathematical logic and foundations |
| Repeated roots and the derivative | Theorem | Commutative algebra |
| Tonelli's theorem | Theorem | Measure and integration |
| Existence of square roots of nonnegative reals | Theorem | Real functions |
| Closure in a metric space | Proposition | General topology |
| Uniqueness of splitting fields | Theorem | Field theory and polynomials |
| Comparison of a series and an integral | Proposition | Real functions |
| Laplace expansion along a column | Theorem | Linear and multilinear algebra; matrix theory |
| Heine–Cantor theorem | Theorem | General topology |
| Solution formula for linear first-order equations | Theorem | Ordinary differential equations |
| Five colour theorem | Theorem | Combinatorics |
| Integral of the exponential function | Proposition | Real functions |
| Dimension of a direct product | Proposition | Linear and multilinear algebra; matrix theory |
| Grassmann's formula | Theorem | Linear and multilinear algebra; matrix theory |
| Spectral theorem | Theorem | Operator theory |
| Classification of finite simple groups | Theorem | Group theory and generalizations |
| Power series of the exponential function | Theorem | Special functions |
| The minimal polynomial divides every polynomial vanishing at the element | Proposition | Field theory and polynomials |
| Every spanning set contains a basis | Theorem | Linear and multilinear algebra; matrix theory |
| Cauchy criterion for series | Theorem | Sequences, series, summability |
| Dimension of the annihilator | Proposition | Linear and multilinear algebra; matrix theory |
| cosh^2 - sinh^2 = 1 | Proposition | Special functions |
| Units of the Gaussian integers | Proposition | Number theory |
| Number of invertible residues modulo n | Proposition | Number theory |
| Continuous functions are Riemann integrable | Theorem | Real functions |
| Existence of Laurent expansions on an annulus | Theorem | Functions of a complex variable |
| Converse of Wilson's theorem | Proposition | Number theory |
| Continuous image of a closed interval is a closed interval | Corollary | Real functions |
| Geometric formula for the dot product | Proposition | Geometry |
| Congruence is compatible with multiplication | Proposition | Number theory |
| Limit of a product of sequences | Proposition | Sequences, series, summability |
| Cyclic groups of the same order are isomorphic | Theorem | Group theory and generalizations |
| Third isomorphism theorem for rings | Theorem | Associative rings and algebras |
| Associativity of matrix multiplication | Proposition | Linear and multilinear algebra; matrix theory |
| Kolmogorov's zero–one law | Theorem | Probability theory and stochastic processes |
| Correspondence between equivalence relations and partitions | Theorem | Mathematical logic and foundations |
| One-sided inverse of a square matrix is two-sided | Proposition | Linear and multilinear algebra; matrix theory |
| The reals have the cardinality of the continuum | Theorem | Mathematical logic and foundations |
| Uniqueness of the derivative | Proposition | Real functions |
| Independent random variables are uncorrelated | Proposition | Probability theory and stochastic processes |
| Determinant of the inverse | Proposition | Linear and multilinear algebra; matrix theory |
| Continuity of the inverse of a strictly monotone continuous function | Theorem | Real functions |
| Classification of finite abelian groups | Theorem | Group theory and generalizations |
| Lcm of coprime integers | Corollary | Number theory |
| Lipschitz maps are uniformly continuous | Proposition | Real functions |
| Cauchy–Hadamard theorem | Theorem | Functions of a complex variable |
| Disjoint cycles commute | Proposition | Group theory and generalizations |
| Composition of surjections is surjective | Proposition | Mathematical logic and foundations |
| Grönwall's inequality | Lemma | Real functions |
| Pépin's test | Theorem | Number theory |
| A function with positive derivative is strictly increasing | Corollary | Real functions |
| i squared is minus one | Proposition | Field theory and polynomials |
| If 2^p − 1 is prime then p is prime | Proposition | Number theory |
| Fermat's Last Theorem for n = 3 | Theorem | Number theory |
| Menelaus's theorem | Theorem | Geometry |
| Heine–Borel theorem | Theorem | General topology |
| Möbius inversion formula | Theorem | Number theory |
| Third isomorphism theorem for vector spaces | Theorem | Linear and multilinear algebra; matrix theory |
| Derivatives of the hyperbolic functions | Proposition | Special functions |
| Young's inequality for products | Theorem | Real functions |
| Derivative of the logarithm | Theorem | Special functions |
| Differentiable functions are continuous | Proposition | Real functions |
| Anticommutativity of the cross product | Proposition | Linear and multilinear algebra; matrix theory |
| Every integer is a square times a square-free integer | Proposition | Number theory |
| Linearity of the integral | Theorem | Real functions |
| Rational root theorem | Theorem | Field theory and polynomials |
| Finite p-groups are nilpotent | Theorem | Group theory and generalizations |
| Holomorphic functions are analytic | Theorem | Functions of a complex variable |
| Absolutely convergent series in a Banach space converge | Theorem | Sequences, series, summability |
| Fundamental theorem of arithmetic | Theorem | Number theory |
| P-adic valuation of a product | Proposition | Number theory |
| Angle bisector theorem | Theorem | Geometry |
| Jordan normal form | Theorem | Linear and multilinear algebra; matrix theory |
| Law of quadratic reciprocity | Theorem | Number theory |
| Fermat's right triangle theorem | Theorem | Number theory |
| Mean of the Poisson distribution | Proposition | Probability theory and stochastic processes |
| Chevalley–Warning theorem | Theorem | Number theory |
| Divergence part of the ratio test | Proposition | Sequences, series, summability |
| Class equation | Theorem | Group theory and generalizations |