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Formula for inverting a Taylor series
In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange–Bürmann formula, gives the Taylor series expansion of the inverse
Lagrange_inversion_theorem
Topics referred to by the same term
four squares of integers Mean value theorem in calculus The Lagrange inversion theorem The Lagrange reversion theorem The method of Lagrangian multipliers
Lagrange's_theorem
Mathematical constant related to the cosine function
f(x)=\cos(x)-x} at π 2 {\textstyle {\frac {\pi }{2}}} (or equivalently, the Lagrange inversion theorem), the Dottie number can be expressed as the infinite series: D
Dottie_number
bound Lagrange form Lagrange form of the remainder Lagrange interpolation Lagrange invariant Lagrange inversion theorem Lagrange multiplier Augmented
List of things named after Joseph-Louis Lagrange
List_of_things_named_after_Joseph-Louis_Lagrange
Multivalued function in mathematics
e − 1. {\displaystyle \int _{0}^{e}W_{0}(x)\,dx=e-1.} By the Lagrange inversion theorem, the Taylor series of the principal branch W 0 ( x ) {\displaystyle
Lambert_W_function
Gives power series for certain implict functions
In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions
Lagrange_reversion_theorem
Attribute of a mathematical function
a residue by series expansion, a major role is played by the Lagrange inversion theorem. Let u ( z ) := ∑ k ≥ 1 u k z k {\displaystyle u(z):=\sum _{k\geq
Residue_(complex_analysis)
Result in enumerative combinatorics and linear algebra
Good who derived it from his multilinear generalization of the Lagrange inversion theorem. MMT was also popularized by Carlitz who found an exponential
MacMahon's_master_theorem
theorem (complex analysis) Identity theorem for Riemann surfaces (Riemann surfaces) Koebe 1/4 theorem (complex analysis) Lagrange inversion theorem (mathematical
List_of_theorems
German mathematician and teacher
discovered the generalized form of the Lagrange inversion theorem. He corresponded and published with Joseph Louis Lagrange and Carl Hindenburg. The compositional
Hans_Heinrich_Bürmann
Polynomials used for interpolation
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data
Lagrange_polynomial
indeterminate forms Abel's theorem – relates the limit of a power series to the sum of its coefficients Lagrange inversion theorem – gives the Taylor series
List_of_real_analysis_topics
Infinite sum of monomials
function of an analytic function can be determined using the Lagrange inversion theorem. The sum of a power series with a positive radius of convergence
Power_series
German mathematician
from the Taylor series for the function itself, related to the Lagrange inversion theorem. In the study of permutations, Rothe was the first to define the
Heinrich_August_Rothe
2009 book on combinatorial enumeration
functions of the classes, in some cases using tools such as the Lagrange inversion theorem as part of the reinterpretation process. The chapters in this
Analytic_Combinatorics_(book)
American mathematician (born 1951)
quasisymmetric functions in 1984 and foundational work on the Lagrange inversion theorem. As of 2017, Gessel was an advisor of 27 Ph.D. students. Gessel
Ira_Gessel
Recreational mathematics planar boundary and area problem
also be written using Bell polynomials, which follows from the Lagrange inversion theorem: r = 2 cos ( π 4 + 1 2 − 1 π + 1 2 ∑ n = 2 ∞ g n ( 1 − 2 π )
Goat_grazing_problem
Mathematical concept
real numbers, it is common to refer to f −1({y}) as a level set. Lagrange inversion theorem, gives the Taylor series expansion of the inverse function of
Inverse_function
Formal power series
T(z)=z\left(1+T(z)^{2}\right)} The Lagrange inversion theorem is a tool used to explicitly evaluate solutions to such equations. Lagrange inversion formula—Let ϕ ( z )
Generating_function
Generalized chain rule in calculus
functionPages displaying short descriptions of redirect targets Lagrange inversion theorem – Formula for inverting a Taylor series Linearity of differentiation –
Faà_di_Bruno's_formula
schoolgirl problem Knapsack problem Kruskal–Katona theorem Lagrange inversion theorem Lagrange reversion theorem Lah number Large number Latin square Levenshtein
Index of combinatorics articles
Index_of_combinatorics_articles
Form of interpolation
_{i=0}^{n}(x-x_{i}).} This parallels the reasoning behind the Lagrange remainder term in the Taylor theorem; in fact, the Taylor remainder is a special case of
Polynomial_interpolation
Integral transform useful in probability theory, physics, and engineering
primes less than a given magnitude, in which he also developed the inversion theorem. Riemann used the Laplace transform to develop the functional equation
Laplace_transform
inversion. He had created an expression for the area under a curve by considering a momentary increase at a point. In effect, the fundamental theorem
History_of_calculus
Decomposition of periodic functions
ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier inversion theorem
Fourier_series
Branch of mathematics that studies the properties of groups
quadratic fields. Early results about permutation groups were obtained by Lagrange, Ruffini, and Abel in their quest for general solutions of polynomial equations
Group_theory
Polynomials in combinatorial mathematics
applications, such as in Faà di Bruno's formula and an explicit formula for Lagrange inversion. The partial or incomplete exponential Bell polynomials are a triangular
Bell_polynomials
German mathematician (1804–1851)
number theory, for example proving Fermat's two-square theorem and Lagrange's four-square theorem, and similar results for 6 and 8 squares. His other work
Carl_Gustav_Jacob_Jacobi
Generalized function whose value is zero everywhere except at zero
Joseph Fourier. Fourier presented what is now called the Fourier integral theorem in his treatise Théorie analytique de la chaleur (1822) in the form: f
Dirac_delta_function
Matrix decomposition
‖ x ‖ = 1 } . {\displaystyle \{\|\mathbf {x} \|=1\}.} By the Lagrange multipliers theorem, u {\displaystyle \mathbf {u} } necessarily satisfies ∇ u
Singular_value_decomposition
Algebraic variety with a group structure
whose underlying variety is a projective variety. Chevalley's structure theorem states that every algebraic group can be constructed from groups in those
Algebraic_group
Regularization technique for ill-posed problems
}}-c\right)} which shows that λ {\displaystyle \lambda } is nothing but the Lagrange multiplier of the constraint. In fact, there is a one-to-one relationship
Ridge_regression
French polymath (1749–1827)
Evaluation of several common definite integrals; General proof of the Lagrange reversion theorem. Laplace built upon the qualitative work of the English polymath
Pierre-Simon_Laplace
Infinite sum that is considered independently from any notion of convergence
case when the coefficient ring is a field of characteristic 0, the Lagrange inversion formula (discussed below) provides a powerful tool to compute the
Formal_power_series
Isometry group of Euclidean space
example, in the case of the group generated by inversion in the origin: the group of all translations and inversion in all points; this is the generalized dihedral
Euclidean_group
Matrix class
b_{ij}=(x_{j}-y_{i})A_{j}(y_{i})B_{i}(x_{j})\,} (Schechter 1959, Theorem 1) where Ai(x) and Bi(x) are the Lagrange polynomials for ( x i ) {\displaystyle (x_{i})} and
Cauchy_matrix
Group that is a topological space with continuous group operations
) ↦ x y {\displaystyle \cdot :G\times G\to G,(x,y)\mapsto xy} and the inversion map: − 1 : G → G , x ↦ x − 1 {\displaystyle ^{-1}:G\to G,x\mapsto x^{-1}}
Topological_group
3D symmetry group
orientation. A4 is the smallest group demonstrating that the converse of Lagrange's theorem is not true in general: given a finite group G and a divisor d of
Tetrahedral_symmetry
Subfield of information theory and computer science
algorithmic information. Instead of proving similar theorems, such as the basic invariance theorem, for each particular measure, it is possible to easily
Algorithmic information theory
Algorithmic_information_theory
(at the time) but incomplete proof of the fundamental theorem of algebra. Joseph Louis Lagrange (1770) The title means "Reflections on the algebraic solutions
List of publications in mathematics
List_of_publications_in_mathematics
Number of integers coprime to and less than n
special case where n is prime is known as Fermat's little theorem. This follows from Lagrange's theorem and the fact that φ(n) is the order of the multiplicative
Euler's_totient_function
Branch of mathematics that studies algebraic structures
theory) Monoid factorisation Syntactic monoid Group (mathematics) Lagrange's theorem (group theory) Subgroup Coset Normal subgroup Characteristic subgroup
List of abstract algebra topics
List_of_abstract_algebra_topics
Physical spaces representing position and momentum, Fourier-transform duals
function and the de Broglie relation are closely related to the Fourier inversion theorem and the concept of frequency domain. Since a free particle has a spatial
Position_and_momentum_spaces
In mathematics, invariant of square matrices
minors: Vandermonde had already given a special case. Immediately following, Lagrange (1773) treated determinants of the second and third order and applied it
Determinant
Central limit theorem Central limit theorem (illustration) – redirects to Illustration of the central limit theorem Central limit theorem for directional
List_of_statistics_articles
Construction in algebra
free of finite rank if H is finite-dimensional: a generalization of Lagrange's theorem for subgroups. As a corollary of this and integral theory, a Hopf
Hopf_algebra
Mathematical version of an order change
with the help of permutations occurred around 1770, when Joseph Louis Lagrange, in the study of polynomial equations, observed that properties of the
Permutation
Approximation method in quantum physics
a basis set ϕ i ( x i ) {\displaystyle \phi _{i}(x_{i})} in which the Lagrange multiplier matrix λ i j {\displaystyle \lambda _{ij}} becomes diagonal
Hartree–Fock_method
Group that is also a differentiable manifold with group operations that are smooth
)} , and taking the opposite angle corresponds to inversion. Thus both multiplication and inversion are differentiable maps. The affine group of one dimension
Lie_group
Problem in celestial mechanics
Heinrich Lambert and formally solved with mathematical proof by Joseph-Louis Lagrange. It has important applications in the areas of rendezvous, targeting, guidance
Lambert's_problem
Topological space that locally resembles Euclidean space
Gauss–Bonnet theorem linked the Euler characteristic to the Gaussian curvature. Investigations of Niels Henrik Abel and Carl Gustav Jacobi on inversion of elliptic
Manifold
Calculus of functions generalization
concepts from differential geometry such as differential forms and Stokes' theorem. This extensive use of linear algebra also allows a natural generalization
Calculus_on_Euclidean_space
function Additive function Dirichlet convolution Erdős–Kac theorem Möbius function Möbius inversion formula Divisor function Liouville function Partition function
List_of_number_theory_topics
Methods for locating real roots of a polynomial
he credited Joseph-Louis Lagrange for this idea, without providing a reference. For making an algorithm of Vincent's theorem, one must provide a criterion
Real-root_isolation
Group of symmetries of a regular polygon
identity and the element rn/2 (with Dn as a subgroup of O(2), this is inversion; since it is scalar multiplication by −1, it is clear that it commutes
Dihedral_group
Experimental design that is optimal with respect to some statistical criterion
of mean-unbiased estimators (under the conditions of the Gauss–Markov theorem). In the estimation theory for statistical models with one real parameter
Optimal_experimental_design
Matrix operation generalizing exponentiation of scalar numbers
characterization indicates that St is given by the Lagrange interpolation formula, so it is the Lagrange−Sylvester polynomial. At the other extreme, if P
Matrix_exponential
Type of group in mathematics
factor of {±1}n acts on the corresponding circle factor of T × {1} by inversion, and the symmetric group Sn acts on both {±1}n and T × {1} by permuting
Orthogonal_group
Discrete group of Möbius transformations
maps. Ahlfors measure conjecture Density theorem for Kleinian groups Ending lamination theorem Tameness theorem (Marden's conjecture) Klein, Felix (1883)
Kleinian_group
principle — infinite-dimensional version of Lagrange multipliers Costate equations — equation for the "Lagrange multipliers" in Pontryagin's minimum principle
List of numerical analysis topics
List_of_numerical_analysis_topics
Number represented as a0+1/(a1+1/...)
Joseph-Louis Lagrange – provided the general solution to Pell's equation using continued fractions similar to Bombelli's 1770 Lagrange – proved that
Simple_continued_fraction
Statistical method
of the bootstrap distribution, but with a different formula (note the inversion of the left and right quantiles): ( θ ( α / 2 ) ∗ , θ ( 1 − α / 2 ) ∗
Bootstrapping_(statistics)
"Smoothing" integral transform
replace u with the formal differentiation operator D = d/dx and utilize the Lagrange shift operator e − y D f ( x ) = f ( x − y ) {\displaystyle e^{-yD}f(x)=f(x-y)}
Weierstrass_transform
Statistic for rank correlation
two items from n items. The number of discordant pairs is equal to the inversion number that permutes the y-sequence into the same order as the x-sequence
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Concept in mathematics
called the Frobenius kernel K. (This is a theorem due to Frobenius (1901); there is still no proof of this theorem that does not use character theory, although
Frobenius_group
Mathematical framework for investment risk
parameter μ {\displaystyle \mu } . This problem is easily solved using a Lagrange multiplier which leads to the following linear system of equations: [ 2
Modern_portfolio_theory
Concept in probability theory and statistics
obtain a sample partial correlation). Note that only a single matrix inversion is required to give all the partial correlations between pairs of variables
Partial_correlation
Lie group of complex numbers of unit modulus; topologically a circle
unit circle). The open balls are circular arcs. Since multiplication and inversion are continuous functions on C × {\displaystyle \mathbb {C} ^{\times
Circle_group
Orientation-preserving mapping class group of the torus
However, the closely related elliptic functions were studied by Joseph Louis Lagrange in 1785, and further results on elliptic functions were published by Carl
Modular_group
alternating series tests), Taylor's theorem (with the Lagrange remainder), Newton's generalized binomial theorem, Euler's complex identity, polar representation
Mathematics education in the United States
Mathematics_education_in_the_United_States
Field of classical mechanics concerned with the motion of spacecraft
follow chaotic orbital paths that require minimal fuel beyond reaching a Lagrange point, with periodic course corrections. Orbits can be plotted from high
Orbital_mechanics
Function whose domain is the positive integers
} Möbius inversion For all k ≥ 4 , r k ( n ) > 0. {\displaystyle k\geq 4,\;\;\;r_{k}(n)>0.} (Lagrange's four-square theorem). r 2 ( n ) = 4
Arithmetic_function
Mathematical space used to study hyperbolic geometry
](\ominus \mathbf {v} \ominus \mathbf {u} )} (gyration inversion law) Some additional theorems satisfied by the Gyration group of any gyrogroup include:
Gyrovector_space
Algebraic structure
under the multiplication, of order q − 1 {\displaystyle q-1} . By Lagrange's theorem, there exists a divisor k {\displaystyle k} of q − 1 {\displaystyle
Finite_field
Group of matrices with determinant 1
with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the
Special_linear_group
Group of flat spacetime symmetries
spacetime dimensions) associated with the Poincaré symmetry, by Noether's theorem, imply 10 conservation laws: 1 for the energy – associated with translations
Poincaré_group
Statistic for rank correlation
or ties. Values range from −1 (100% negative association, or perfect inversion) to +1 (100% positive association, or perfect agreement). A value of zero
Goodman_and_Kruskal's_gamma
Error-correcting codes
procedures that produce a systematic Reed–Solomon code. One method uses Lagrange interpolation to compute polynomial p m {\displaystyle p_{m}} such that
Reed–Solomon_error_correction
Periodicity computation method
elements), then that matrix is an identity matrix times a constant, so the inversion is trivial. The latter is the case when the sample times are equally spaced
Least-squares spectral analysis
Least-squares_spectral_analysis
Measure of the asymmetry of random variables
Estimation of Skewness and Kurtosis Comparison of skew estimators by Kim and White. Closed-skew Distributions — Simulation, Inversion and Parameter Estimation
Skewness
Double cover Lie group of the special orthogonal group
multiplication is continuous, and the group axioms are satisfied with inversion being continuous, making Spin ( n ) {\displaystyle \operatorname {Spin}
Spin_group
Type of mathematical object
equivalent conditions, such as conjugation inducing a trivial action, or inversion map ι being a group scheme automorphism. Given a group G, one can form
Group_scheme
Set of the values of a function
a functionPages displaying short descriptions of redirect targets Set inversion – Mathematical problem of finding the set mapped by a specified function
Image_(mathematics)
Approach to public-key cryptography
of E ( F q ) {\displaystyle E(\mathbb {F} _{q})} , it follows from Lagrange's theorem that the number h = 1 n | E ( F q ) | {\displaystyle h={\frac {1}{n}}|E(\mathbb
Elliptic-curve_cryptography
Table that displays the frequency of variables
level. Its values range from −1.0 (100% negative association, or perfect inversion) to +1.0 (100% positive association, or perfect agreement). A value of
Contingency_table
American mathematician
"Chronological Bibliography of the Cauchy Integral Theorem" listing 200 proofs of the famous theorem was coauthored with Herbert K. Fallin. The bibliography
Henry_W._Gould
Concept in mathematical group theory
the inversions in circles. This group is also known as the Möbius group. In Euclidean space En, n > 2, the conformal group is generated by inversions in
Conformal_group
Techniques to maintain quantum coherence
{\displaystyle \epsilon (t)} using the calculus of variations introducing Lagrange multipliers. A new objective functional is defined J ′ = J + ∫ 0 T ⟨ χ
Coherent_control
Probability distribution
skew-t) OWENS: Owen's T Function Archived 2010-06-14 at the Wayback Machine Closed-skew Distributions - Simulation, Inversion and Parameter Estimation
Skew_normal_distribution
Exact statistical hypothesis test
rewritten for every case. Are primarily used to provide a p-value. The inversion of the test to get confidence regions/intervals requires even more computation
Permutation_test
Direction and rate of rotation
pseudoscalar, a numerical quantity which changes sign under a parity inversion, such as inverting one axis or switching the two axes. In three-dimensional
Angular_velocity
Physical object which does not deform when forces or moments are exerted on it
applies for S2n, of which the case n = 1 is inversion symmetry. For a (rigid) rectangular transparent sheet, inversion symmetry corresponds to having on one
Rigid_body
Statistical technique
objective function subject to the m constraints. It is solved by the use of Lagrange multipliers. After some algebraic manipulations, the result is obtained
Total_least_squares
Finite difference method for numerically solving parabolic differential equations
tridiagonal matrix algorithm in favor over the much more costly matrix inversion. A quasilinear equation, such as (this is a minimalistic example and not
Crank–Nicolson_method
Approximation of the definite integral of a function
less, we can interpolate it exactly using n interpolation points with Lagrange polynomials li(x), where l i ( x ) = ∏ j ≠ i x − x j x i − x j . {\displaystyle
Gaussian_quadrature
Vector used in astronomy
}{dt}}} and where the triple cross product has been simplified using Lagrange's formula r × ( r × d r d t ) = r ( r ⋅ d r d t ) − r 2 d r d t . {\displaystyle
Laplace–Runge–Lenz_vector
Branch of mathematical analysis
definition is used. The corresponding derivative is calculated using Lagrange's rule for differential operators. To find the αth order derivative, the
Fractional_calculus
Formulation of quantum mechanics
eiPs = eD, the exponential of a derivative operator is a translation (so Lagrange's shift operator). The X operator likewise generates translations in P.
Matrix_mechanics
Matrix representing a Euclidean rotation
To incorporate the constraint(s), we may employ a standard technique, Lagrange multipliers, assembled as a symmetric matrix, Y. Thus our method is: Differentiate
Rotation_matrix
Complex-valued arithmetic function
have order 2, and imaginary characters have order 3 or greater. By Lagrange's theorem the order of a character divides the order of ( Z / m Z ) × ^ {\displaystyle
Dirichlet_character
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
Boy/Male
Indian, Kannada
Creator; Creative; Invention
Boy/Male
Hindu
Invention
Boy/Male
Biblical
The God of conversion.
Girl/Female
Biblical
Conversion, captivity.
Boy/Male
American, Australian, Latin
Crowned with Laurel; From Laurentium; Laurentium was a City South of Rome Known for Its Numerous Laurel Trees
Boy/Male
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Telugu
Invention; Create; Written
Surname or Lastname
English and French
English and French : topographic name for someone who lived by a granary, from Middle English, Old French grange (Latin granica ‘granary’, ‘barn’, from granum ‘grain’). In some cases, the surname has arisen from places named with this word, for example in Dorset and West Yorkshire in England, and in Ardèche and Jura in France. The Marquis de Lafayette owned a property named Lagrange, and there used to be a place in VT so named in his honor.
Girl/Female
Biblical
Captivity, conversion, old age.
Biblical
conversion; captivity
Boy/Male
American, Australian, British, English
From the Barley Grange
Surname or Lastname
English
English : variant spelling of Lawrence.
Boy/Male
Hindu, Indian, Marathi, Sanskrit, Tamil
Invention
Surname or Lastname
English and Scottish
English and Scottish : patronymic from the Old Norse personal name Ãvarr, a compound of either Ãv ‘yew tree’, ‘bow’ or Ing (the name of a god) + ar ‘warrior’ or ‘spear’.Swedish equivalent of Iversen 1.Respelling of Danish, Norwegian, and North German Iversen.
Boy/Male
Tamil
Invention
Boy/Male
American, British, English
From the Barley Grange
Surname or Lastname
English
English : variant spelling of Lawrence.
Boy/Male
Biblical
Respiration, conversion, taking captive.
Biblical
invention; industry
Girl/Female
Arabic
Invention; Discovery
Girl/Female
Biblical
Invention, industry.
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
Boy/Male
German
Divine Helmut; Divine Protection
Boy/Male
Indian, Punjabi, Sikh
Absorbed in Adoration
Boy/Male
British, English
Oath of God
Girl/Female
Hindu
The first finger
Male
Scandinavian
Scandinavian form of German Werner, VERNER means "Warin warrior," i.e. "covered warrior."
Girl/Female
Gujarati, Hindu, Indian
Young One
Surname or Lastname
English
English : variant of Sermon.
Boy/Male
Arabic, Muslim
Light of Ali
Female
Hebrew
(יְמִימָה) Variant spelling of Hebrew Yemiymah, YEMIMA means "dove."Â
Boy/Male
English
Hard boar.
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
LAGRANGE INVERSION-THEOREM
n.
An account or description from a particular point of view, especially as contrasted with another account; as, he gave another version of the affair.
n.
The faculty of inventing; imaginative faculty; skill or ingenuity in contriving anything new; as, a man of invention.
n.
The act of inserting; as, the insertion of scions in stocks; the insertion of words or passages in writings.
n.
A translation; that which is rendered from another language; as, the Common, or Authorized, Version of the Scriptures (see under Authorized); the Septuagint Version of the Old Testament.
n.
The condition or mode of being inserted or attached; as, the insertion of stamens in a calyx.
n.
A running into; hence, an entering into a territory with hostile intention; a temporary invasion; a predatory or harassing inroad; a raid.
n.
The act of immersing, or the state of being immersed; a sinking within a fluid; a dipping; as, the immersion of Achilles in the Styx.
n.
A straining, stretching, or bending; the state of being strained; as, the intension of a musical string.
n.
An appropriation of, and dealing with the property of another as if it were one's own, without right; as, the conversion of a horse.
n.
The state of being turned back or outward; as, eversion of eyelids; ectropium.
n.
That which is invented; an original contrivance or construction; a device; as, this fable was the invention of Esop; that falsehood was her own invention.
n.
The incoming or first attack of anything hurtful or pernicious; as, the invasion of a disease.
n.
A warlike or hostile entrance into the possessions or domains of another; the incursion of an army for conquest or plunder.
n.
A hostile or predatory incursion; an inroad or incursion of mounted men; a sudden and rapid invasion by a cavalry force; a foray.
n.
A change of form, direction, or the like; transformation; conversion; turning.
n.
A change or reduction of the form or value of a proposition; as, the conversion of equations; the conversion of proportions.
v. t.
To adjust or settle; to prepare; to determine; as, to arrange the preliminaries of an undertaking.
n.
The act of turning aside from any course, occupation, or object; as, the diversion of a stream from its channel; diversion of the mind from business.
n.
The act of finding out or inventing; contrivance or construction of that which has not before existed; as, the invention of logarithms; the invention of the art of printing.
n.
The act of immediate inference, by which we deny the opposite of anything which has been affirmed; as, all men are mortal; then, by obversion, no men are immortal. This is also described as "immediate inference by privative conception."