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Infinitesimal

Definition

In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinitieth" item in a sequence.

Related concepts

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Tall David Tall Dedekind-infinite set Definable number Definable real number Derivative Detlef Laugwitz Differential (infinitesimal)Differential (mathematics)Differential calculus Differential equation Differential form Differential geometry of curves Differential geometry of surfaces Differential operator Differentiation rules Dimension Dirac delta function Direct comparison test Directional derivative Dirichlet's test Disc integration Divergence Divergence theorem Division algebra Division by zero Dual-complex number Dual number Dual quaternion E (mathematical constant)Eddington number Edward Nelson Edwin Hewitt Eisenstein integer Eleatic School Epsilon number Erkenntnis Euler substitution Euler–Maclaurin formula Exponential function Extended natural numbers Extended real number line Exterior algebra Exterior derivative Extreme value theorem Factorial Fast-growing hierarchy Finite difference First-order logic First derivative test Fluxion Fluxion (mathematics)Fourier series Free variables and bound variables Friedman's SSCG function Fundamental Theorem of Line Integrals Fundamental theorem of calculus Fuzzy number Gabriel's horn Galileo's paradox Gaussian integer Gaussian rational General Leibniz rule Generality of algebra Generalized Stokes' theorem Geometric algebra Geometric calculus Geometric series Georg Cantor George Berkeley Gimel function Giuseppe Veronese Googol Googolplex Gottfried Leibniz Gottfried Wilhelm Leibniz Gradient Graham's number Graph of a function Greek mathematics Green's theorem Grzegorczyk hierarchy HOPOS Hardy hierarchy Harmonic series (mathematics)Hermann Cohen Hessian matrix Hilbert's paradox of the Grand Hotel Hilbert space History of calculus History of large numbers Howard Jerome Keisler Hyperbolic quaternion Hypercomplex number Hyperfinite set Hyperinteger Hyperoperation Hyperreal number Hyperreal numbers Implicit differentiation Increment theorem Indefinite and fictitious numbers Indeterminate form Infinite series Infinite set Infinitesimal calculus Infinitesimal strain theory Infinitesimal transformation Infinity Infinity (philosophy)Infinity symbol Instant Integer Integral Integral calculus Integral equation Integral of secant cubed Integral of the secant function Integral symbol Integral test for convergence Integration Bee Integration by parts Integration by substitution Integro-differential equation Internal set Internal set theory Intuitionistic logic Inverse function rule Irrational number Isaac Newton Jacobian matrix and determinant Jerzy Łoś Johannes Kepler John Wallis Joseph-Louis Lagrange Journal for Research in Mathematics Education Karl Weierstrass Keith Stroyan Knuth's up-arrow notation Kruskal's tree theorem L'Hôpital's rule Lagrange multiplier Laplace operator Large cardinal Large numbers Largest known prime number Laurent series Law of Continuity Law of continuity Law of excluded middle Lazare Carnot Leibniz's notation Leibniz integral rule Leonhard Euler Levi-Civita field Limit (mathematics)Limit comparison test Limit of a function Limit of a sequence Lindeberg's condition Line integral Linear algebra Linear function Linear order Linearity of differentiation List of integrals of exponential functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of inverse trigonometric functions List of integrals of irrational algebraic functions List of integrals of logarithmic functions List of integrals of rational functions List of integrals of trigonometric functions List of limits List of numbers List of types of numbers Lists of integrals Logarithmic derivative Long and short scales Maclaurin series Manifold Marburg school Mathematics Matrix calculus Maximum and minimum Mean value theorem Method of Fluxions Method of exhaustion Method of indivisibles Method of normals Microcontinuity Mikhail Katz Model theory Monad (nonstandard analysis)Multicomplex number Multiple integral Multiplicative inverse Multivariable calculus Möbius plane Möbius transformation Names of large numbers Natural logarithm Natural number Neo-Kantianism Neo-Latin Newton's method Newton's notation for differentiation Nicholas of Cusa Nicolaus Mercator Nigel Cutland Nilpotent Nonstandard analysis Nonstandard calculus Normal number Notation for differentiation Number Numeral (linguistics)Octonion One-sided limit Order of approximation Ordered field Orders of magnitude (numbers)Ordinal number Ordinary differential equation Overspill P-adic number Paradoxes of infinity Paradoxes of set theory Parallelogram Partial derivative Partial differential equation Partial fractions in integration Paul du Bois-Reymond Period (algebraic geometry)Pierre de Fermat Plane-based geometric algebra Point at infinity Power of 10 Power of three Power of two Power rule Power series Precalculus Probability space Product rule Profinite integer Projectively extended real line Proof that 22/7 exceeds π Proper class Quadratic integral Quantification (logic)Quaternion Quotient rule Radian Random variable Ratio test Rational number Rayo's number Real Analysis Exchange Real closed field Real number Regiomontanus' angle maximization problem Related rates René Descartes Reviel Netz Richard Dedekind Riemann integral Riemann sphere Riemannian manifold Rigour Robert Goldblatt Rolle's theorem Root test Rudolf Carnap Scientific notation Secant line Second derivative Second derivative test Sedenion Sequence Set (mathematics)Set theory Shannon number Shell integration Silvanus P. Thompson Simon Stevin Sine Skewes's number Slope Slow-growing hierarchy Smooth infinitesimal analysis Solenoid (mathematics)Spacetime algebra Sphere at infinity Split-biquaternion Split-complex number Split-octonion Split-quaternion Standard part function Stanford Encyclopedia of Philosophy Stationary point Steinhaus–Moser notation Steinmetz solid Stirling's approximation Stochastic differential equation Stokes' theorem Sum rule in differentiation Supernatural number Superreal number Supertask Surface integral Surreal number Synthetic differential geometry Tangent Tangent half-angle substitution Taylor's theorem Taylor series Telescoping series Tensor Tensor calculus Term test Tetration The Analyst The Mathematics Enthusiast The Method of Mechanical Theorems Thomas Mormann Thoralf Skolem Thought experiment Transcendental functions Transcendental law of homogeneity Transcendental number Transfer principle Transfinite number Transseries Trapezoidal rule Trigintaduonion Trigonometric substitution Tullio Levi-Civita Ultrafilter Ultrapower Veblen function Vector calculus Vladimir Arnold Volume integral Wilhelmus Luxemburg ZFC Zeno's dichotomy paradox Zeno of Elea Émile Borel ∞

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