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Mapping function
mathematics, an additive set function is a function μ \mu mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the
Sigma-additive_set_function
Algebraic structure of set algebra
of a statistical trial or experiment Sigma-additive set function – Mapping function Sigma-ring – Family of sets closed under countable unions Elstrodt
Σ-algebra
Generalization of mass, length, area and volume
∈ Σ , μ ( E ) ≥ 0 {\displaystyle E\in \Sigma ,\ \ \mu (E)\geq 0} Countable additivity (or σ-additivity): For all countable collections { E k } k =
Measure_(mathematics)
Topics referred to by the same term
addition operation Additive set-function see Sigma additivity Additive category, a preadditive category with finite biproducts Additive inverse, an arithmetic
Additive
Function from sets to numbers
mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values
Set_function
Class of convex shapes
an atom-free vector-valued sigma-additive set function. Here, a function from a family of sets to vectors is sigma-additive when the family is closed under
Zonoid
Cadlag in probability theory
{B(\alpha _{t}+i\sigma _{t}u,\beta _{t}-i\sigma u)}{B(\alpha _{t},\beta _{t})}}\right)^{\delta _{t}}e^{i\mu _{t}u}\;\;.} Two subcases of additive logistic process
Additive_process
Statistical regression model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an
Additive_model
Property of certain measures on topological spaces
field of measure theory, τ-additivity is a certain property of measures on topological spaces. A measure or set function μ {\displaystyle \mu } on a
Tau_additivity
Statistics models class
generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some
Generalized_additive_model
Method for converting signals between digital and analog
Delta-sigma (ΔΣ; or sigma-delta, ΣΔ) modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency
Delta-sigma_modulation
Set of real numbers that is not Lebesgue measurable
However, the closest generalization to mass must have the property of sigma additivity, which leads us to the Lebesgue measure. It assigns a measure of b
Vitali_set
Probability distribution
cumulative distribution function is F X ( x ) = Φ ( ln x − μ σ ) {\displaystyle F_{X}(x)=\Phi {\left({\frac {\ln x-\mu }{\sigma }}\right)}} where Φ {\displaystyle
Log-normal_distribution
Topics referred to by the same term
Harish-Chandra's σ function Weierstrass sigma function Sigma additivity Sigma (album) Sigma (DJs), a British drum and bass duo Universal Sigma, a Japanese record
Sigma_(disambiguation)
Concept in real analysis
is the set of discontinuities of the derivative of a differentiable function if and only if it is a meagre F σ {\displaystyle F_{\sigma }} set. In particular
Continuously differentiable function of a single real variable
Continuously_differentiable_function_of_a_single_real_variable
Mathematical term; concerning axioms used to derive theorems
logical structure, used also in theoretical computer science. It consists of a set of formal statements known as axioms that are used for the logical deduction
Axiomatic_system
Family of probability distributions
models are both additive and reproductive; we thus have the duality transformation Y ↦ Z = Y / σ 2 . {\displaystyle Y\mapsto Z=Y/\sigma ^{2}.} A third
Tweedie_distribution
not a result. A cylinder set measure can be intuitively understood as defining a finitely additive function on the cylinder sets of the topological vector
Cylinder_set_measure
Function whose domain is the positive integers
is no prime number that divides both of them. Then an arithmetic function a is additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n;
Arithmetic_function
Property of some mathematical functions
particularly norms and square roots. Additive maps are special cases of subadditive functions. A subadditive function is a function f : A → B {\displaystyle f\colon
Subadditivity
Theorem extending pre-measures to measures
{\displaystyle \sigma } -finite), and moreover that it does not fail to satisfy the sigma-additivity of the original function. For a given set Ω , {\displaystyle
Carathéodory's extension theorem
Carathéodory's_extension_theorem
Generalization of a measure
additive, and the measure may even be identically zero even if the content is not. First restrict the content to compact sets. This gives a function λ
Content_(measure_theory)
Measure of local oscillation behavior
E\in \Sigma } Definition 1.3. The variation (also called absolute variation) of the signed measure μ {\displaystyle \mu } is the set function | μ | (
Total_variation
Statistics function
{y-\mu }{\sigma }}} . Other definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also
Q-function
Class of Banach spaces
{\displaystyle ba(\Sigma )} of an algebra of sets Σ {\displaystyle \Sigma } is the Banach space consisting of all bounded and finitely additive signed measures
Ba_space
club set stratified A formula of set theory is stratified if and only if there is a function σ {\displaystyle \sigma } which sends each variable appearing
Glossary_of_set_theory
Average uncertainty in variable's states
properties of entropy as a function of random variables (subadditivity and additivity), rather than the properties of entropy as a function of the probability
Entropy_(information_theory)
Nineteenth letter in the Greek alphabet
function τ(n) related to the divisor function σ(n), also sometimes called Ramanujan's tau function. "DLMF: §27.14 Unrestricted Partitions ‣ Additive Number
Tau
Fundamental theorem in probability theory and statistics
{N}}\left(0,\sigma ^{2}\right).} In the case σ > 0 , {\displaystyle \sigma >0,} convergence in distribution means that the cumulative distribution functions of
Central_limit_theorem
Probability distribution
probability density function is f ( x ) = 1 2 π σ 2 exp ( − ( x − μ ) 2 2 σ 2 ) . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\exp {\left(-{\frac
Normal_distribution
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Designing products to facilitate manufacturing
of the given additive manufacturing machine, material, and process (for example, less than 70 degrees from vertical). Design for Six Sigma Design for X
Design_for_manufacturability
Function spaces generalizing finite-dimensional p norm spaces
{\displaystyle A_{j}\in \Sigma } has finite measure and 1 A j {\displaystyle {\mathbf {1} }_{A_{j}}} is the indicator function of the set A j , {\displaystyle
Lp_space
Concept in economics
In economics, additive utility is a cardinal utility function with the sigma additivity property. Additivity (also called linearity or modularity) means
Additive_utility
Mathematical series
form a ring Ω, indeed an R-algebra, with the zero function as additive zero element and the function δ defined by δ(1) = 1, δ(n) = 0 for n > 1 as multiplicative
Dirichlet_series
Four-dimensional number system
-i\,\sigma _{1}=-\sigma _{2}\,\sigma _{3},\quad \mathbf {j} \mapsto -i\,\sigma _{2}=-\sigma _{3}\,\sigma _{1},\quad \mathbf {k} \mapsto -i\,\sigma _{3}=-\sigma
Quaternion
Process of finding a spatial transformation that aligns two point clouds
log-likelihood function, i.e. the cost function: Ignoring constants independent of θ {\displaystyle \theta } and σ {\displaystyle \sigma } , Equation (cpd
Point-set_registration
Function equal to the product of its values on coprime factors
ω ( n ) {\displaystyle \gamma (n)=(-1)^{\omega (n)}} , where the additive function ω ( n ) {\displaystyle \omega (n)} is the number of distinct primes
Multiplicative_function
Measure of linear correlation
with an additive normal noise (i.e., y= a + bx + e), then a standard error associated to the correlation is σ r ≈ 1 − r 2 n {\displaystyle \sigma _{r}\approx
Pearson correlation coefficient
Pearson_correlation_coefficient
Axiom of set theory
{\displaystyle (\forall x^{\sigma })(\exists y^{\tau })R(x,y)\to (\exists f^{\sigma \to \tau })(\forall x^{\sigma })R(x,f(x)).} Unlike in set theory, the axiom
Axiom_of_choice
Statistical measure of how far values spread from their average
variable with itself, and it is often represented by σ 2 {\displaystyle \sigma ^{2}} , s 2 {\displaystyle s^{2}} , Var ( X ) {\displaystyle \operatorname
Variance
Family of sets closed under countable unions
In mathematics, a nonempty collection of sets is called a 𝜎-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation
Sigma-ring
Mathematical model of ferromagnetism in statistical mechanics
σ ) {\displaystyle Z_{\beta }=\sum _{\sigma }e^{-\beta H(\sigma )}} is the partition function. For a function f {\displaystyle f} of the spins ("observable")
Ising_model
Points with no three in a line
cap set problem is the problem of finding the size of the largest possible cap set, as a function of n {\displaystyle n} . The first few cap set sizes
Cap_set
Left-invariant (or right-invariant) measure on locally compact topological group
limit exists follows using Tychonoff's theorem. The function μ A {\displaystyle \mu _{A}} is additive on disjoint compact subsets of G {\displaystyle G}
Haar_measure
Family closed under subsets and countable unions
algebra 𝜎-ring – Family of sets closed under countable unions Sigma additivity – Mapping functionPages displaying short descriptions of redirect targets Bauer
Sigma-ideal
Probability distribution
function is f ( x ∣ ν , σ ) = x σ 2 exp ( − ( x 2 + ν 2 ) 2 σ 2 ) I 0 ( x ν σ 2 ) H ( x ) , {\displaystyle f(x\mid \nu ,\sigma )={\frac {x}{\sigma ^{2}}}\exp
Rice_distribution
Algebraic ring that need not have additive negative elements
which the additive monoid is a complete monoid, meaning that it has an infinitary sum operation Σ I {\displaystyle \Sigma _{I}} for any index set I {\displaystyle
Semiring
Process of mapping a continuous set to a countable set
denotes the ceiling function). The essential property of a quantizer is having a countable set of possible output values smaller than the set of possible input
Quantization (signal processing)
Quantization_(signal_processing)
Set of statistical processes for estimating the relationships among variables
a function (regression function) of X i {\displaystyle X_{i}} and β {\displaystyle \beta } , with e i {\displaystyle e_{i}} representing an additive error
Regression_analysis
f} is subadditive. The maximum of additive set functions is subadditive (dually, the minimum of additive functions is superadditive). Formally, for each
Subadditive_set_function
Set of probability distributions
=A'(\theta )\,,\quad \operatorname {Var} [Y]=\sigma ^{2}A''(\theta )=\sigma ^{2}V(\mu )\,\!,} with unit variance function V ( μ ) = A ″ ( ( A ′ ) − 1 ( μ ) ) {\displaystyle
Exponential_dispersion_model
Integral using products instead of sums
which are sigma-additive set functions. However, the Type I integral is not multiplicative as a functional. Given two product-integrable functions f , g
Product_integral
Subject in mathematics
{\displaystyle \nu :{\mathcal {E}}(X,G)\to \mathbb {R} +} is a σ-additive function, i.e. ν {\displaystyle \nu } is a measure. Let Γ ⊂ X ∗ {\displaystyle
Measure theory in topological vector spaces
Measure_theory_in_topological_vector_spaces
Measure of quantum entanglement in quantum mechanics
measures. is additive on tensor products: E N ( ρ ⊗ σ ) = E N ( ρ ) + E N ( σ ) {\displaystyle E_{N}(\rho \otimes \sigma )=E_{N}(\rho )+E_{N}(\sigma )} is not
Negativity (quantum mechanics)
Negativity_(quantum_mechanics)
Everywhere except a set of measure zero
everywhere in X {\displaystyle X} if there exists a measurable set N ∈ Σ {\displaystyle N\in \Sigma } with μ ( N ) = 0 {\displaystyle \mu (N)=0} , and all x
Almost_everywhere
Theorem in Optimal Transport
where p {\displaystyle p} is a smooth real function defined on Ω {\displaystyle \Omega } , unique up to an additive constant, and w {\displaystyle w} is a
Polar_factorization_theorem
Generalization of finite measure to Banach spaces
countably additive functions taking values respectively on the real interval [ 0 , ∞ ) , {\displaystyle [0,\infty ),} the set of real numbers, and the set of
Vector_measure
Concept in mathematics
E\in \Sigma .} In particular, the set function E ↦ ∫ E f d μ {\displaystyle E\mapsto \int _{E}f\,\mathrm {d} \mu } defines a countably-additive B {\displaystyle
Bochner_integral
Probability distribution
parameter, such as a mean value, in a setting where the data are observed with additive errors. If (as in nearly all practical statistical work) the population
Student's_t-distribution
All numbers between two given numbers
{X}}-2\sigma _{\bar {X}}\leq \mu \leq {\bar {X}}+2\sigma _{\bar {X}})\approx 0.95.} If the value of the standard deviation σ X ¯ {\displaystyle \sigma _{\bar
Interval_(mathematics)
Iterative method for finding maximum likelihood estimates in statistical models
{\mu }}_{1},{\boldsymbol {\mu }}_{2},\Sigma _{1},\Sigma _{2}{\big )},} where the incomplete-data likelihood function is L ( θ ; x ) = ∏ i = 1 n ∑ j = 1 2
Expectation–maximization algorithm
Expectation–maximization_algorithm
Branch of statistics to estimate models based on measured data
{\displaystyle A} with additive white Gaussian noise (AWGN) w [ n ] {\displaystyle w[n]} with zero mean and known variance σ 2 {\displaystyle \sigma ^{2}} (i.e.
Estimation_theory
Method of data analysis
\mathbf {\Sigma } ^{\mathsf {T}}\mathbf {U} ^{\mathsf {T}}\mathbf {U} \mathbf {\Sigma } \mathbf {W} ^{\mathsf {T}}\\&=\mathbf {W} \mathbf {\Sigma } ^{\mathsf
Principal_component_analysis
Set function that is a precursor to a measure
measure" and "set function", respectively. Outer measures are not, in general, measures, since they may fail to be σ {\displaystyle \sigma } -additive.) Hahn-Kolmogorov
Pre-measure
Theoretical object in mathematics
not zero. Deitmar suggested that F1 should be found by forgetting the additive structure of a ring and focusing on the multiplication. Toën and Vaquié
Field_with_one_element
Generalized notion of measure in mathematics
(X,\Sigma )} (that is, a set X {\displaystyle X} with a σ-algebra Σ {\displaystyle \Sigma } on it), an extended signed measure is a set function μ : Σ
Signed_measure
Differential equations involving stochastic processes
] → R n × m ; {\displaystyle \sigma :\mathbb {R} ^{n}\times [0,T]\to \mathbb {R} ^{n\times m};} be measurable functions for which there exist constants
Stochastic differential equation
Stochastic_differential_equation
Mathematical construction used in homotopy theory
simplicial set X are the images in that simplicial set of the morphisms σ n , 0 , … , σ n , n : [ n + 1 ] → [ n ] {\displaystyle \sigma ^{n,0},\dotsc ,\sigma ^{n
Simplicial_set
Number, approximately 3.14
μ ) 2 / ( 2 σ 2 ) . {\displaystyle f(x)={1 \over \sigma {\sqrt {2\pi }}}\,e^{-(x-\mu )^{2}/(2\sigma ^{2})}.} The factor of 1 2 π {\displaystyle {\tfrac
Pi
Notion in measure theory
level sets of a function. Theorem. Suppose ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu )} is complete. Then ( X , Σ , μ ) {\displaystyle (X,\Sigma ,\mu
Lifting_theory
Mathematical statistics distance measure
reality from a model may be estimated, to within a constant additive term, by a function of the deviations observed between data and the model's predictions
Kullback–Leibler_divergence
Concept in measure theory
\mu } is called a σ {\displaystyle \sigma } -finite measure if the set X {\displaystyle X} is σ {\displaystyle \sigma } -finite. A finite measure, for instance
Σ-finite_measure
Expected value of a random variable given that certain conditions are known to occur
{\mathcal {H}}} is a sub σ {\displaystyle \sigma } -algebra of F {\displaystyle {\mathcal {F}}} , the function X : Ω → R n {\displaystyle X\colon \Omega
Conditional_expectation
\Sigma } is a σ {\displaystyle \sigma } -algebra of sets. Ξ {\displaystyle \Xi } is an algebra of sets (for spaces only requiring finite additivity, such
List_of_Banach_spaces
Signal processing phenomenon
noise where the noise amplitude scales with the signal's intensity. Unlike additive noise, which is independent of the signal, multiplicative noise complicates
Multiplicative_noise
Function which is integrable on its domain
set in the Euclidean space R n {\textstyle \mathbb {R} ^{n}} and f : Ω → C {\textstyle f:\Omega \to {\mathbb {C}}} be a Lebesgue measurable function.
Locally_integrable_function
Notion in statistics
\theta _{m}}}\Sigma ^{-1}{\frac {\partial \mu }{\partial \theta _{n}}}+{\frac {1}{2}}\operatorname {tr} \left(\Sigma ^{-1}{\frac {\partial \Sigma }{\partial
Fisher_information
Antioxidant
categories in catalogues and databases, such as food additive, household product ingredient, industrial additive, personal care product and cosmetic ingredient
Butylated_hydroxytoluene
Mathematical function
of measurable sets and countably additive measures. Carathéodory's work on outer measures found many applications in measure-theoretic set theory (outer
Outer_measure
Class of statistical models
_{ij}} is a random variable describing additive noise. An example of such a model with an exponential mean function fitted to longitudinal measurements of
Nonlinear_mixed-effects_model
1932 book by John von Neumann
recover additivity when averaging over the hidden parameters. For example, for a spin-1/2 system, measurements of ( σ x + σ y ) {\displaystyle (\sigma _{x}+\sigma
Mathematical Foundations of Quantum Mechanics
Mathematical_Foundations_of_Quantum_Mechanics
Mathematical construction relating to infinite-dimensional spaces
extend to a countably additive measure on the σ {\displaystyle \sigma } -algebra generated by the collection of cylinder sets in H {\displaystyle H}
Abstract_Wiener_space
Type of group in abstract algebra
over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular
Symmetric_group
Measure with complex values
{\displaystyle (X,\Sigma )} is a complex-valued function μ : Σ → C {\displaystyle \mu :\Sigma \to \mathbb {C} } that is sigma-additive. In other words,
Complex_measure
Set theory concept
exists a κ {\displaystyle \kappa } -additive, non-trivial, 0-1-valued measure μ {\displaystyle \mu } on the power set of κ {\displaystyle \kappa } . Here
Measurable_cardinal
Mode of convergence of an infinite series
real-valued function ‖ ⋅ ‖ : G → R + {\textstyle \|\cdot \|:G\to \mathbb {R} _{+}} on an abelian group G {\displaystyle G} (written additively, with identity
Absolute_convergence
Representation of a type of random process
(X_{t+n}X_{t})-\mu ^{2}={\frac {\sigma _{\varepsilon }^{2}}{1-\varphi ^{2}}}\,\,\varphi ^{|n|}.} It can be seen that the autocovariance function decays with a decay
Autoregressive_model
Structure-preserving map between two algebraic structures of the same type
{\displaystyle \Sigma _{1}} and Σ 2 {\displaystyle \Sigma _{2}} , a function h : Σ 1 ∗ → Σ 2 ∗ {\displaystyle h\colon \Sigma _{1}^{*}\to \Sigma _{2}^{*}} such
Homomorphism
Method of mathematical integration
simple function can be written in different ways as a linear combination of indicator functions, but the integral will be the same by the additivity of measures
Lebesgue_integral
Branch of statistics mathematics
{\displaystyle \mu } and Σ {\displaystyle \Sigma } are continuous functions and then the covariance function Σ {\displaystyle \Sigma } defines a covariance operator
Functional_data_analysis
Generalization of the Cartesian product
written additively, it may also be called the direct sum of two groups, denoted by G ⊕ H . {\displaystyle G\oplus H.} It is defined as follows: the set of
Direct_product
as a function of time. This response function is called creep defined by J ( t ) ≡ ϵ ( t ) / σ 0 {\displaystyle J(t)\equiv \epsilon (t)/\sigma _{0}}
Anelasticity
Branch of functional analysis
\rangle } is a countably additive measure on the Borel sets E of R. In the above formula 1E denotes the indicator function of E. These measures νξ are
Borel_functional_calculus
Function that "converges" to periodicity
not quasiperiodic. Additive synthesis Aperiodic function Computer music Fourier series Harmonic series (music) Quasiperiodic function Quasiperiodic tiling
Almost_periodic_function
Model of intermolecular interactions
components are set up by changing at least one potential interaction parameter ( ε {\displaystyle \varepsilon } or σ {\displaystyle \sigma } ) of one of
Lennard-Jones_potential
Mathematical method for optimizing material layout under given conditions
designs ready for additive manufacturing. A stiff structure is one that has the least possible displacement when given certain set of boundary conditions
Topology_optimization
:\mathbf {A} \to X} be an additive set function. If μ {\displaystyle \mu } is weakly countably additive, then it is countably additive (in the original topology
Orlicz–Pettis_theorem
Deep learning generative model to encode data representation
, σ ) {\displaystyle N(x|\mu ,\sigma )} which is parameterized by μ {\displaystyle \mu } and σ {\displaystyle \sigma } respectively, and as a member
Variational_autoencoder
Type of vector space in math
spaces are function spaces associated to measure spaces (X, M, μ), where X is a set, M is a σ-algebra of subsets of X, and μ is a countably additive measure
Hilbert_space
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
Girl/Female
Scottish
Listener.
Boy/Male
Hindu, Indian, Muslim
Powerful; Mighty; Strong; Rich; Successful
Female
Egyptian
, an uncertain goddess.
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, a sister of Sekherta.
Girl/Female
Arabic, Muslim
Peace
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Surname or Lastname
English
English : variant spelling of See.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Girl/Female
Latin
Sign.
Boy/Male
Norse
Victorious defender.
Girl/Female
Afghan, Arabic, Armenian, Australian, Farsi, French, Gujarati, Hebrew, Hindu, Indian, Malayalam, Muslim, Sanskrit, Tamil
Limit; Border; Listener; Precious Thing; Treasure; Boundary; Bank; Shore
Female
Egyptian
, a sister of Sekherta.
Male
English
Short form of English Stephen, STE means "crown."
Girl/Female
Danish, German, Latin, Scandinavian, Swedish
Sign; Signal; Victory
Girl/Female
Hindu
Boundary, Border
Girl/Female
British, Danish, English, German, Swedish
Powerful Silence; Peaceful Victory
Female
Hindi/Indian
(सीमा) Hindi name SIMA means "boundary, limit." Compare with another form of Sima.
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
Boy/Male
Tamil
Victory, One who always win
Surname or Lastname
English
English : variant spelling of Ruston.Norwegian : habitational name from any of several farmsteads in eastern Norway named from rust ‘slope with trees’, ‘hill’, ‘ridge’.
Boy/Male
Tamil
Cause, With a treasure, Receptacle
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Goddess Durga; One of the Powerful Pandavas in Mahabharata; Name of River
Boy/Male
Tamil
Shubhashis | à®·à¯à®ªà®¾à®·à®¿à®¸Â
Blessing
Surname or Lastname
English
English : unexplained. In the US this is a southern name, common in TX, MS, and LA.
Boy/Male
Spanish Hebrew English
Supplanter.
Boy/Male
British, English
A Planet
Girl/Female
Bengali, Indian
Hemanta Season
Female
English
English variant spelling of Latin Charis, CARIS means "grace."
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
SIGMA ADDITIVE-SET-FUNCTION
pl.
of Sigma
v. t.
A point so connected by any law whatever with another point, called an index, that as the index moves in any manner in a plane the first point or stigma moves in a determinate way in the same plane.
n.
A stigma. See Stigma, n., 6 (a) & (b).
a.
Answering to an interrogative or inquiry; conveying a reply; as, redditive words.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
a.
Additive.
n.
The Greek letter /, /, or / (English S, or s). It originally had the form of the English C.
n.
See Set, n., 2 (e) and 3.
a.
Established; prescribed; as, set forms of prayer.
pl.
of Stigma
v. i.
To fit or suit one; to sit; as, the coat sets well.
adv.
In addition; further; besides; over and above; still.
a.
Pertaining to adoption; made or acquired by adoption; fitted to adopt; as, an adoptive father, an child; an adoptive language.
n.
Anything added; increase; augmentation; as, a piazza is an addition to a building.
pl.
of Stigma
imp. & p. p.
of Set
a.
Regular; uniform; formal; as, a set discourse; a set battle.
n.
That which is set, placed, or fixed.
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.