WordNet Search - 3.1

Key: "S:" = Show Synset (semantic) relations, "W:" = Show Word (lexical) relations

Display options for sense: (gloss) "an example sentence"

- S: (n) irrational number,
**irrational**(a real number that cannot be expressed as a rational number)

- S: (adj)
**irrational**(not consistent with or using reason)*"irrational fears"; "irrational animals"* - S: (adj)
**irrational**(real but not expressible as the quotient of two integers)*"irrational numbers"* *domain category*- S: (n) mathematics, math, maths (a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement)
*direct hyponym*/*full hyponym**domain category***domain term category**- S: (adj) idempotent (unchanged in value following multiplication by itself)
*"this matrix is idempotent"* - S: (adj) combinatorial (relating to the combination and arrangement of elements in sets)
- S: (adj) continuous (of a function or curve; extending without break or irregularity)
- S: (adj) discontinuous (of a function or curve; possessing one or more discontinuities)
- S: (adj) solid (having three dimensions)
*"a cube is a solid figure with six sides"* - S: (adj) commutative ((11) )
- S: (adj) indeterminate ((of a quantity) having no definite value, as an equation that cannot be solved)
*"0/0 is an indeterminate form"* - S: (adj) direct (similar in nature or effect or relation to another quantity)
*"a term is in direct proportion to another term if it increases (or decreases) as the other increases (or decreases)"* - S: (adj) inverse (opposite in nature or effect or relation to another quantity)
*"a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)"* - S: (adj) dividable (can be divided usually without leaving a remainder)
*"15 is dividable by 3"* - S: (adj) undividable, indivisible by (cannot be divided without leaving a remainder)
- S: (adj) mathematical (characterized by the exactness or precision of mathematics)
*"mathematical precision"* - S: (adj) round ((mathematics) expressed to the nearest integer, ten, hundred, or thousand)
*"in round numbers"* - S: (adj) representable (expressible in symbolic form)
*"uniquely representable in the form..."* - S: (adj) linear, additive (designating or involving an equation whose terms are of the first degree)
- S: (adj) bilinear (linear with respect to each of two variables or positions)
- S: (adj) nonlinear (designating or involving an equation whose terms are not of the first degree)
- S: (adj) monotonic, monotone (of a sequence or function; consistently increasing and never decreasing or consistently decreasing and never increasing in value)
- S: (adj) nonmonotonic (not monotonic)
- S: (adj) open ((set theory) of an interval that contains neither of its endpoints)
- S: (adj) closed ((set theory) of an interval that contains both its endpoints)
- S: (adj) nonnegative (either positive or zero)
- S: (adj) positive (greater than zero)
*"positive numbers"* - S: (adj) negative (less than zero)
*"a negative number"* - S: (adj) disjoint (having no elements in common)
- S: (adj) noninterchangeable (such that the terms of an expression cannot be interchanged without changing the meaning)
*"the arguments of the symmetric relation, `is the father of', are noninterchangeable"* - S: (adj) invariant (unaffected by a designated operation or transformation)
- S: (adj) affine ((mathematics) of or pertaining to the geometry of affine transformations)
- S: (adj) analytic (using or subjected to a methodology using algebra and calculus)
*"analytic statics"* - S: (adj) diagonalizable (capable of being transformed into a diagonal matrix)
- S: (adj) scalene (of a triangle having three sides of different lengths)
- S: (adj) isometric (related by an isometry)
- S: (adj) differential (involving or containing one or more derivatives)
*"differential equation"* - S: (adj) rational (capable of being expressed as a quotient of integers)
*"rational numbers"* - S: (adj)
**irrational**(real but not expressible as the quotient of two integers)*"irrational numbers"* - S: (adj) prime (of or relating to or being an integer that cannot be factored into other integers)
*"prime number"* - S: (adj) binomial (of or relating to or consisting of two terms)
*"binomial expression"* - S: (adj) bivariate (having two variables)
*"bivariate binomial distribution"* - S: (adj) cubic (involving the cube and no higher power of a quantity or variable)
*"a cubic equation"* - S: (adj) quadratic (involving the second and no higher power of a quantity or degree)
*"quadratic equation"* - S: (adj) biquadratic (involving the fourth and no higher power of a quantity or degree)
- S: (n) rounding, rounding error ((mathematics) a miscalculation that results from rounding off numbers to a convenient number of decimals)
*"the error in the calculation was attributable to rounding"; "taxes are rounded off to the nearest dollar but the rounding error is surprisingly small"* - S: (n) truncation error ((mathematics) a miscalculation that results from cutting off a numerical calculation before it is finished)
- S: (n) mathematical process, mathematical operation, operation ((mathematics) calculation by mathematical methods)
*"the problems at the end of the chapter demonstrated the mathematical processes involved in the derivation"; "they were learning the basic operations of arithmetic"* - S: (n) rationalization, rationalisation ((mathematics) the simplification of an expression or equation by eliminating radicals without changing the value of the expression or the roots of the equation)
- S: (n) invariance (the nature of a quantity or property or function that remains unchanged when a given transformation is applied to it)
*"the invariance of the configuration under translation"* - S: (n) accuracy ((mathematics) the number of significant figures given in a number)
*"the atomic clock enabled scientists to measure time with much greater accuracy"* - S: (n) symmetry, symmetricalness, correspondence, balance ((mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane)
- S: (n) asymmetry, dissymmetry, imbalance ((mathematics) a lack of symmetry)
- S: (n) factorization, factorisation, factoring ((mathematics) the resolution of an expression into factors such that when multiplied together they give the original expression)
- S: (n) extrapolation ((mathematics) calculation of the value of a function outside the range of known values)
- S: (n) interpolation ((mathematics) calculation of the value of a function between the values already known)
- S: (n) rule, formula ((mathematics) a standard procedure for solving a class of mathematical problems)
*"he determined the upper bound with Descartes' rule of signs"; "he gave us a general formula for attacking polynomials"* - S: (n) recursion ((mathematics) an expression such that each term is generated by repeating a particular mathematical operation)
- S: (n) invariant (a feature (quantity or property or function) that remains unchanged when a particular transformation is applied to it)
- S: (n) quantity (the concept that something has a magnitude and can be represented in mathematical expressions by a constant or a variable)
- S: (n) polynomial, multinomial (a mathematical function that is the sum of a number of terms)
- S: (n) series ((mathematics) the sum of a finite or infinite sequence of expressions)
- S: (n) infinitesimal ((mathematics) a variable that has zero as its limit)
- S: (n) fractal ((mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry)
- S: (n) arithmetic (the branch of pure mathematics dealing with the theory of numerical calculations)
- S: (n) geometry (the pure mathematics of points and lines and curves and surfaces)
- S: (n) affine geometry (the geometry of affine transformations)
- S: (n) elementary geometry, parabolic geometry, Euclidean geometry ((mathematics) geometry based on Euclid's axioms)
- S: (n) Euclid's axiom, Euclid's postulate, Euclidean axiom ((mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry)
- S: (n) fractal geometry ((mathematics) the geometry of fractals)
*"Benoit Mandelbrot pioneered fractal geometry"* - S: (n) non-Euclidean geometry ((mathematics) geometry based on axioms different from Euclid's)
*"non-Euclidean geometries discard or replace one or more of the Euclidean axioms"* - S: (n) hyperbolic geometry ((mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane)
*"Karl Gauss pioneered hyperbolic geometry"* - S: (n) elliptic geometry, Riemannian geometry ((mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle)
*"Bernhard Riemann pioneered elliptic geometry"* - S: (n) numerical analysis ((mathematics) the branch of mathematics that studies algorithms for approximating solutions to problems in the infinitesimal calculus)
- S: (n) spherical geometry ((mathematics) the geometry of figures on the surface of a sphere)
- S: (n) spherical trigonometry ((mathematics) the trigonometry of spherical triangles)
- S: (n) analytic geometry, analytical geometry, coordinate geometry (the use of algebra to study geometric properties; operates on symbols defined in a coordinate system)
- S: (n) plane geometry (the geometry of 2-dimensional figures)
- S: (n) solid geometry (the geometry of 3-dimensional space)
- S: (n) projective geometry, descriptive geometry (the geometry of properties that remain invariant under projection)
- S: (n) trigonometry, trig (the mathematics of triangles and trigonometric functions)
- S: (n) algebra (the mathematics of generalized arithmetical operations)
- S: (n) quadratics (a branch of algebra dealing with quadratic equations)
- S: (n) linear algebra (the part of algebra that deals with the theory of linear equations and linear transformation)
- S: (n) vector algebra (the part of algebra that deals with the theory of vectors and vector spaces)
- S: (n) matrix algebra (the part of algebra that deals with the theory of matrices)
- S: (n) calculus, infinitesimal calculus (the branch of mathematics that is concerned with limits and with the differentiation and integration of functions)
- S: (n) analysis (a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation)
- S: (n) differential calculus, method of fluxions (the part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential)
- S: (n) integral calculus (the part of calculus that deals with integration and its application in the solution of differential equations and in determining areas or volumes etc.)
- S: (n) calculus of variations (the calculus of maxima and minima of definite integrals)
- S: (n) set theory (the branch of pure mathematics that deals with the nature and relations of sets)
- S: (n) subgroup ((mathematics) a subset (that is not empty) of a mathematical group)
- S: (n) group theory (the branch of mathematics dealing with groups)
- S: (n) Galois theory (group theory applied to the solution of algebraic equations)
- S: (n) topology, analysis situs (the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions)
- S: (n) metamathematics (the logical analysis of mathematical reasoning)
- S: (n) binomial ((mathematics) a quantity expressed as a sum or difference of two terms; a polynomial with two terms)
- S: (n) proof (a formal series of statements showing that if one thing is true something else necessarily follows from it)
- S: (n) equation (a mathematical statement that two expressions are equal)
- S: (n) formula, expression (a group of symbols that make a mathematical statement)
- S: (n) mathematical statement (a statement of a mathematical relation)
- S: (n) recursive definition ((mathematics) a definition of a function from which values of the function can be calculated in a finite number of steps)
- S: (n) boundary condition ((mathematics) a condition specified for the solution to a set of differential equations)
- S: (n) set ((mathematics) an abstract collection of numbers or symbols)
*"the set of prime numbers is infinite"* - S: (n) domain, domain of a function ((mathematics) the set of values of the independent variable for which a function is defined)
- S: (n) image, range, range of a function ((mathematics) the set of values of the dependent variable for which a function is defined)
*"the image of f(x) = x^2 is the set of all non-negative real numbers if the domain of the function is the set of all real numbers"* - S: (n) universal set ((mathematics) the set that contains all the elements or objects involved in the problem under consideration)
*"all other sets are subsets of the universal set"* - S: (n) mathematical space, topological space ((mathematics) any set of points that satisfy a set of postulates of some kind)
*"assume that the topological space is finite dimensional"* - S: (n) field ((mathematics) a set of elements such that addition and multiplication are commutative and associative and multiplication is distributive over addition and there are two elements 0 and 1)
*"the set of all rational numbers is a field"* - S: (n) matrix ((mathematics) a rectangular array of quantities or expressions set out by rows and columns; treated as a single element and manipulated according to rules)
- S: (n) diagonal ((mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry)
- S: (n) arithmetic progression ((mathematics) a progression in which a constant is added to each term in order to obtain the next term)
*"1-4-7-10-13- is the start of an arithmetic progression"* - S: (n) geometric progression ((mathematics) a progression in which each term is multiplied by a constant in order to obtain the next term)
*"1-4-16-64-256- is the start of a geometric progression"* - S: (n) harmonic progression ((mathematics) a progression of terms whose reciprocals form an arithmetic progression)
- S: (n) mathematician (a person skilled in mathematics)
- S: (n) cardinality ((mathematics) the number of elements in a set or group (considered as a property of that grouping))
- S: (n) complex number, complex quantity, imaginary number, imaginary ((mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1)
- S: (n) radical ((mathematics) a quantity expressed as the root of another quantity)
- S: (n) mathematical relation (a relation between mathematical expressions (such as equality or inequality))
- S: (n) function, mathematical function, single-valued function, map, mapping ((mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function))
- S: (n) expansion (a function expressed as a sum or product of terms)
*"the expansion of (a+b)^2 is a^2 + 2ab + b^2"* - S: (n) metric function, metric (a function of a topological space that gives, for any two points in the space, a value equal to the distance between them)
- S: (n) transformation ((mathematics) a function that changes the position or direction of the axes of a coordinate system)
- S: (n) reflection ((mathematics) a transformation in which the direction of one axis is reversed)
- S: (n) rotation ((mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin)
- S: (n) translation ((mathematics) a transformation in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same)
- S: (n) affine transformation ((mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis)
- S: (n) operator ((mathematics) a symbol or function representing a mathematical operation)
- S: (n) parity ((mathematics) a relation between a pair of integers: if both integers are odd or both are even they have the same parity; if one is odd and the other is even they have different parity)
*"parity is often used to check the integrity of transmitted data"* - S: (n) transitivity ((logic and mathematics) a relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third)
- S: (n) reflexivity, reflexiveness ((logic and mathematics) a relation such that it holds between an element and itself)
- S: (n) additive inverse ((mathematics) one of a pair of numbers whose sum is zero; the additive inverse of -5 is +5)
- S: (n) multiplicative inverse, reciprocal ((mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7)
- S: (n) plane, sheet ((mathematics) an unbounded two-dimensional shape)
*"we will refer to the plane of the graph as the X-Y plane"; "any line joining two points on a plane lies wholly on that plane"* - S: (n) geodesic, geodesic line ((mathematics) the shortest line between two points on a mathematically defined surface (as a straight line on a plane or an arc of a great circle on a sphere))
- S: (n) parallel ((mathematics) one of a set of parallel geometric figures (parallel lines or planes))
*"parallels never meet"* - S: (n) upper bound ((mathematics) a number equal to or greater than any other number in a given set)
- S: (n) lower bound ((mathematics) a number equal to or less than any other number in a given set)
- S: (n) ray ((mathematics) a straight line extending from a point)
- S: (n) osculation ((mathematics) a contact of two curves (or two surfaces) at which they have a common tangent)
- S: (v) develop (expand in the form of a series)
*"Develop the function in the following form"* - S: (v) iterate (run or be performed again)
*"the function iterates"* - S: (v) commute, transpose (exchange positions without a change in value)
*"These operators commute with each other"* - S: (v) rationalize, rationalise (remove irrational quantities from)
*"This function can be rationalized"* - S: (v) eliminate (remove (an unknown variable) from two or more equations)
- S: (v) calculate, cipher, cypher, compute, work out, reckon, figure (make a mathematical calculation or computation)
- S: (v) extract (calculate the root of a number)
- S: (v) interpolate, extrapolate (estimate the value of)
- S: (v) differentiate (calculate a derivative; take the derivative)
- S: (v) integrate (calculate the integral of; calculate by integration)
- S: (v) prove (prove formally; demonstrate by a mathematical, formal proof)
- S: (v) truncate (approximate by ignoring all terms beyond a chosen one)
*"truncate a series"* - S: (v) reduce (simplify the form of a mathematical equation of expression by substituting one term for another)
- S: (v) converge (approach a limit as the number of terms increases without limit)
- S: (v) diverge (have no limits as a mathematical series)
- S: (v) osculate (have at least three points in common with)
*"one curve osculates the other"; "these two surfaces osculate"* *direct hypernym*/*inherited hypernym*/*sister term**derivationally related form**pertainym**antonym*