| Matrix exponential of a sum, commuting and non-commuting cases | Theorem | Linear and multilinear algebra; matrix theory |
| Dedekind zeta function | Definition | Number theory |
| Every nonzero natural number is a successor | Theorem | Mathematical logic and foundations |
| A tree with at least two vertices has at least two leaves | Proposition | Combinatorics |
| Attainable null space | Concept | Functional analysis |
| Locally cyclic group | Concept | |
| Variety of algebras | Definition | General algebraic systems |
| Maximum and minimum | Definition | Real functions |
| Fourier sine and cosine series of a function on an interval | Theorem | Harmonic analysis on Euclidean spaces |
| Linearity of the Laplace transform | Proposition | Integral transforms, operational calculus |
| K5 is not planar | Theorem | Combinatorics |
| Increasing and decreasing function on an open interval | Concept | Real functions |
| Unique size of a nonempty finite set | Theorem | Mathematical logic and foundations |
| General solution of a second order equation with complex characteristic roots | Theorem | Ordinary differential equations |
| Periodic point | Definition | Dynamical systems and ergodic theory |
| Capacity of a set | Definition | Potential theory |
| Multiplication by zero | Lemma | Mathematical logic and foundations |
| Critical number | Concept | Real functions |
| Nonzero subspaces of R^n have a basis and a well-defined dimension | Theorem | Linear and multilinear algebra; matrix theory |
| Rank–nullity theorem for matrices | Theorem | Linear and multilinear algebra; matrix theory |
| Monotonic law for multiplication of integers | Theorem | Order, lattices, ordered algebraic structures |
| One is a two-sided multiplicative identity of the natural numbers | Lemma | Mathematical logic and foundations |
| Z-transform | Definition | Integral transforms, operational calculus |
| Associativity of multiplication of natural numbers | Theorem | Mathematical logic and foundations |
| Addition of integers is commutative, associative and cancellative | Theorem | Number theory |
| Commutativity of multiplication of natural numbers | Theorem | Mathematical logic and foundations |
| Monotonic law for addition of natural numbers | Theorem | Mathematical logic and foundations |
| Picard's theorem for systems with continuous partial derivatives | Theorem | Ordinary differential equations |
| General solution of x'' = Ax with distinct nonpositive eigenvalues | Theorem | Ordinary differential equations |
| Schröder–Bernstein theorem for finite sets | Proposition | Mathematical logic and foundations |
| Orthogonality of eigenfunctions of the equation x'' + lambda x = 0 with standard boundary conditions | Theorem | Ordinary differential equations |
| Existence and uniqueness for second-order linear initial value problems | Theorem | Ordinary differential equations |
| Group ring | Definition | Associative rings and algebras |
| Root system | Definition | Nonassociative rings and algebras |
| Attainable null space | Definition | Functional analysis |
| Convolution of central binomial coefficients | Corollary | Combinatorics |
| Ratio and root limits give the radius of convergence | Theorem | Functions of a complex variable |
| Recurrence for the falling factorial | Lemma | Combinatorics |
| Transitivity of the pair relation for constructing the integers | Lemma | Number theory |
| Oscillation of a function | Definition | Real functions |
| Topological manifold | Definition | Manifolds and cell complexes |
| Division with remainder for natural numbers | Theorem | Number theory |
| Concave up and concave down | Concept | Real functions |
| Addition and multiplication of rationals respect equality | Theorem | Number theory |
| No surjection from the positive integers onto the unit interval | Proposition | Mathematical logic and foundations |
Math 2.0