6,052 articles
Zeilberger algorithm
The Zeilberger algorithm, also known as creative telescoping or the Gosper-Zeilberger algorithm, is a computer algebra method, devised by Doron Zeilberger in 1990, that proves definite hypergeometric summation identities.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory (ZF) is the standard axiom system for set theory, the foundation for modern mathematics; with the axiom of choice it is ZFC.
Zero
Zero, denoted 0, is the additive identity of arithmetic, an integer that is neither positive nor negative, whose oldest dated written form appears in Cambodia in AD 683.
Zero density estimates
A zero-density estimate bounds how many zeros of an L-function, such as the Riemann zeta function, lie to the right of a vertical line Re(s) = σ.
Zero divisor
A zero divisor is a nonzero element of a ring that gives zero when multiplied by another nonzero element, as 2 · 3 = 0 in the integers modulo 6.
Zero sharp
Zero sharp (0#) is a real number in set theory whose existence, a large-cardinal hypothesis, implies the universe V is very different from the constructible universe L.
Zero to the power of zero
Zero to the power of zero, written 0⁰, is the expression with both base and exponent zero, defined as 1 in combinatorics and computing standards but indeterminate in real analysis.
Zero-based numbering
Zero-based numbering, also called zero-based indexing, is the convention of counting a sequence from zero rather than one, standard in C-family languages and defended by Dijkstra's 1982 note EWD 831.
Zero-free region
A zero-free region is a domain near the line Re(s) = 1 of the complex plane where an L-function such as the Riemann zeta function is proved to have no zeros.
Zero–one law (first-order logic)
The zero–one law in first-order logic says any fixed first-order sentence holds on a random graph with probability tending to 0 or 1, proved in 1969 and 1976.
Zeros of the Riemann zeta function
The zeros of the Riemann zeta function are the complex values where ζ(s) = 0: trivial zeros at negative even integers and non-trivial zeros in the critical strip.
Zeroth-order optimization
Zeroth-order optimization is a family of methods that minimizes a function using only its function values, with no derivative information, applied in adversarial attacks and language model fine-tuning.
Zeta function regularization
Zeta function regularization is a summation technique that assigns finite values to divergent sums and products, famously giving 1+2+3+… = −1/12, and is used in quantum field theory.
Zhang's theorem on bounded gaps
Zhang's theorem on bounded gaps is Yitang Zhang's 2013 proof that infinitely many consecutive prime pairs differ by less than 70 million, the first finite bound on prime gaps.
Zipf's law
Zipf's law, or the Zipfian distribution, states that a word's frequency in a text is roughly inversely proportional to its rank, named for George Kingsley Zipf.
Zoia Ceaușescu
Zoia Ceaușescu, also known as Zoe Ceaușescu (1949–2006), was a Romanian mathematician, the only daughter of Nicolae and Elena Ceaușescu, who researched functional analysis and led INCREST's mathematics section.
Zonotope
A zonotope is a convex polytope expressible as the Minkowski sum of finitely many line segments, equivalently a linear projection of a higher-dimensional cube; every face is centrally symmetric.
Zorn's lemma
Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a set-theoretic principle equivalent to the axiom of choice, used to prove that every vector space has a basis.
Γ-convergence
Γ-convergence is a notion of convergence for sequences of functionals, introduced by Ennio De Giorgi in 1975, designed so that minima and minimizers of variational problems converge well.
μ-calculus
The μ-calculus, also called the modal μ-calculus, is a temporal logic extending modal logic with least and greatest fixpoint operators, defined by Dexter Kozen in 1983.
π-calculus
The π-calculus is a process calculus for concurrent systems where processes pass channel names, allowing communication structure to change; developed by Milner, Parrow, and Walker in the late 1980s.
Σ-algebra (σ-field)
A σ-algebra, also called a σ-field, is a collection of subsets of a set closed under complementation and countable unions, the domain on which measures are defined.