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Quickly growing function
the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is
Ackermann_function
German mathematician (1896–1962)
work in mathematical logic and the Ackermann function, an important example in the theory of computation. Ackermann was born in Herscheid, Germany, and
Wilhelm_Ackermann
One of several equivalent definitions of a computable function
recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other
General_recursive_function
Well-quasi-ordering of finite trees
phenomenally fast as a function of n {\displaystyle n} , far faster than any primitive recursive function or the Ackermann function, for example.[citation
Kruskal's_tree_theorem
Generalization of addition, multiplication, exponentiation, tetration, etc.
rule part of the definition, as in Knuth's up-arrow version of the Ackermann function: a [ n ] b = a [ n − 1 ] ( a [ n ] ( b − 1 ) ) , n ≥ 1 {\displaystyle
Hyperoperation
Topics referred to by the same term
objects named after Wilhelm Ackermann Ackermann coding Ackermann function Ackermann ordinal Ackermann set theory Ackermann steering geometry, in mechanical
Ackermann
function Mathieu function Mittag-Leffler function Painlevé transcendents Parabolic cylinder function Arithmetic–geometric mean Ackermann function: in the theory
List of mathematical functions
List_of_mathematical_functions
Means of expressing certain extremely large numbers
3=g_{3}(2)=g_{2}^{2}(1)=g_{2}(g_{2}(1))=f^{f(1)}(1)=f^{a^{b}}(1)} The Ackermann function can be expressed using Conway chained arrow notation: A ( m , n )
Conway_chained_arrow_notation
Mathematical function that can be computed by a program
same function within a definition be to arguments that are smaller in some well-partial-order on the function's domain. For instance, for the Ackermann function
Computable_function
Arithmetic operation
tetration in Wiktionary, the free dictionary. Ackermann function Big O notation Double exponential function Hyperoperation Iterated logarithm Symmetric
Tetration
Exponential function of an exponential function
faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow faster. See Big
Double_exponential_function
Data structure for storing non-overlapping sets
required is O(mα(n)), where α(n) is the extremely slow-growing inverse Ackermann function. Although disjoint-set forests do not guarantee this time per operation
Disjoint-set_data_structure
Sudan function is an example of a function that is recursive, but not primitive recursive. This is also true of the better-known Ackermann function. In
Sudan_function
Concept in theoretical computer science
recursive function that computes their score (computes σ), thus providing a lower bound for Σ. This function's growth is comparable to that of Ackermann's function
Busy_beaver
Function computable with bounded loops
primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known
Primitive_recursive_function
Simple programming languages
Turing-complete language and can express all computable functions. For example, it can express the Ackermann function, which (not being primitive recursive) cannot
BlooP_and_FlooP
Ordinal-indexed family of rapidly increasing functions
recursive function is dominated by fω, which is a variant of the Ackermann function. For n ≥ 3, the set E n {\displaystyle {\mathcal {E}}^{n}} in the
Fast-growing_hierarchy
Minimum spanning forest algorithm that greedily adds edges
α(V)) for this loop, where α is the extremely slowly growing inverse Ackermann function. This part of the time bound is much smaller than the time for the
Kruskal's_algorithm
Numbers significantly larger than those used regularly
extremely large numbers: Knuth's up-arrow notation, hyperoperators, Ackermann function, including tetration Conway chained arrow notation Steinhaus-Moser
Large_numbers
Branch of mathematical combinatorics
enormously large – bounds that grow exponentially, or even as fast as the Ackermann function are not uncommon. In some small niche cases, upper and lower bounds
Ramsey_theory
Large number coined by Ronald Graham
the rapidly growing Ackermann function A(n, n). (In fact, f ( n ) > A ( n , n ) {\displaystyle f(n)>A(n,n)} for all n.) The function f can also be expressed
Graham's_number
Arithmetic operation
named hyperoperation. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster
Exponentiation
Growth of quantities at rate proportional to the current amount
tetration, and A ( n , n ) {\displaystyle A(n,n)} , the diagonal of the Ackermann function. In reality, initial exponential growth is often not sustained forever
Exponential_growth
Elementary operation on a natural number
ISBN 978-3-319-68397-3. Halmos, Chapter 11 Rubtsov, C.A.; Romerio, G.F. (2004). "Ackermann's Function and New Arithmetical Operations" (PDF). Paul R. Halmos (1968). Naive
Successor_function
Theorem in mathematical logic
non-primitive recursive functions such as the Ackermann function. It dominates every computable function provably total (see partial function) in Peano arithmetic
Paris–Harrington_theorem
Rapid growth of the complexity of a problem due to its combinatorial properties
functions, the analysis of some puzzles and games, and some pathological examples[further explanation needed] which can be modelled as the Ackermann function
Combinatorial_explosion
Programming language
nesting depth. An example of a total computable function that is not LOOP-computable is the Ackermann function. The LOOP language was formulated in a 1967
LOOP_(programming_language)
increasing) function; in particular, Ackermann function. Simple function: a real-valued function over a subset of the real line, similar to a step function. Measurable
List_of_types_of_functions
Describes approximate behavior of a function
notation is a mathematical notation that describes the approximate size of a function on a domain. Big O is a member of a family of notations invented by the
Big_O_notation
the Ackermann function. Raphael M. Robinson called functions of two natural number variables G(n, x) double recursive with respect to given functions, if
Double_recursion
Method of notation of very large integers
by a function involving the first four hyperoperators;. Then, f ω ( x ) {\displaystyle f_{\omega }(x)} is comparable to the Ackermann function, f ω +
Knuth's_up-arrow_notation
Computational problem with high complexity
{\displaystyle f(n)=A(n,n)=F_{\omega }(n)} , where A {\displaystyle A} is the Ackermann function. In other words, A C K := F ω {\displaystyle {\mathsf {ACK}}:={\mathsf
Nonelementary_problem
Romanian mathematician
mathematician, known for the Sudan function, an important example in the theory of computation, similar to the Ackermann function. Born in Bucharest, Sudan received
Gabriel_Sudan
Total order in computer science
also be systems for certain general recursive functions, for example a system for the Ackermann function may contain the rule A(a+, b+) → A(a, A(a+, b))
Path ordering (term rewriting)
Path_ordering_(term_rewriting)
less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize 1970 = number of compositions of two types of 9
1000_(number)
Theorem about natural numbers
}(m_{k})}(3))\cdots ))-2} . Some examples: (For Ackermann function and Graham's number bounds see fast-growing hierarchy § Functions in fast-growing hierarchies.) Goodstein's
Goodstein's_theorem
Set-theoretic function
{\displaystyle f_{\psi (\Omega ^{\omega })}(n)} is comparable with the Ackermann function A ( n , n ) {\displaystyle A(n,n)} , and f ψ ( ε Ω + 1 ) ( n ) {\displaystyle
Ordinal_collapsing_function
Study of computable functions and Turing degrees
arithmetic proves that functions like the Ackermann function, which are not primitive recursive, are total. Not every total computable function is provably total
Computability_theory
Inverse function to a tower of powers
{\displaystyle n{\sqrt {\log ^{*}n}}.} Inverse Ackermann function, an even more slowly growing function also used in computational complexity theory Cormen
Iterated_logarithm
Least-weight tree connecting graph vertices
α(m,n)), where α is the classical functional inverse of the Ackermann function. The function α grows extremely slowly, so that for all practical purposes
Minimum_spanning_tree
Method for finding minimum spanning trees
on Borůvka's and runs in O(E α(E,V)) time, where α is the inverse Ackermann function. These randomized and deterministic algorithms combine steps of Borůvka's
Borůvka's_algorithm
Topics referred to by the same term
significance level of a statistical test (symbol "α") The inverse Ackermann function α, sometimes used as a placeholder for ordinal numbers ALPHA, a particle
Alpha_(disambiguation)
Use of functions that call themselves
include divide-and-conquer algorithms such as Quicksort, and functions such as the Ackermann function. All of these algorithms can be implemented iteratively
Recursion_(computer_science)
American computer scientist and mathematician
was the first to prove the optimal runtime involving the inverse Ackermann function. Tarjan received the Turing Award jointly with John Hopcroft in 1986
Robert_Tarjan
Sequence with limited alternation of symbols
inverse Ackermann function α(n) = min { m | A(m,m) ≥ n }, where A is the Ackermann function. Due to the very rapid growth of the Ackermann function, its
Davenport–Schinzel_sequence
Coding language, extension for Erlang
function: (defun ackermann ((0 n) (+ n 1)) ((m 0) (ackermann (- m 1) 1)) ((m n) (ackermann (- m 1) (ackermann m (- n 1))))) Composing functions: (defun compose
LFE_(programming_language)
Problem in math and computer science
to be complete for Ackermann function time complexity. In 2022 reachability in vector addition systems was shown to be Ackermann-complete and therefore
Reachability_problem
Maximal subgraph whose vertices can reach each other
\alpha } is a very slowly growing inverse of the very quickly growing Ackermann function. One application of this sort of incremental connectivity algorithm
Component_(graph_theory)
multiplication, exponentiation, tetration, etc. The Ackermann function is an example of a function that is not primitive recursive, showing that PR is
PR_(complexity)
Notation for extremely large numbers
3\rightarrow 64\rightarrow 2<f^{64}(4)={\text{Graham's number}}.} Ackermann function Hugo Steinhaus, Mathematical Snapshots, Oxford University Press 19693
Steinhaus–Moser_notation
Sudan: known for the Sudan function, an important example in the theory of computation, similar to the Ackermann function. Ion Tănăsescu: he discovered
List of Romanian inventors and discoverers
List_of_Romanian_inventors_and_discoverers
Algorithmic problem of finding non-crossing drawings
In the edge-arrival case, there is an asympotically tight inverse-Ackermann function update-time algorithm due to La Poutré, improving upon algorithms
Planarity_testing
Maximal biconnected subgraph
edge additions in O(m α(m, n)) total time, where α is the inverse Ackermann function. This time bound is proved to be optimal. Uzi Vishkin and Robert Tarjan
Biconnected_component
English mathematician (1912–1985)
as second-order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the
Reuben_Goodstein
maps Logistic map Lorenz attractor Lorenz-96 Iterated function system Tetration Ackermann function Horseshoe map Hénon map Arnold's cat map Population dynamics
List of dynamical systems and differential equations topics
List_of_dynamical_systems_and_differential_equations_topics
Attempts to formalize the concept of algorithms
as μ-operator or mu-operator) because Ackermann (1925) produced a hugely growing function—the Ackermann function—and Rózsa Péter (1935) produced a general
Algorithm_characterizations
Mathematical object
defining lookup constructs to implement such “strong” functions like the Ackermann function. Algebraic data type Catamorphism Anamorphism Philip Wadler:
Initial_algebra
Wiki-based programming chrestomathy
on Rosetta Code include: "99 Bottles of Beer" (song) Abbreviations Ackermann function Amicable numbers Anagrams Bernoulli numbers Bitwise operations Cholesky
Rosetta_Code
Any planar graph can be subdivided by removing a few vertices
O(n\alpha (n))} where α ( n ) {\displaystyle \alpha (n)} is the inverse Ackermann function. Single-source inter-part distances: The distances computed in the
Planar_separator_theorem
weak lower bound is AA(187196)(1), where A(n) is a version of the Ackermann function. Mathematics: SSCG(3): appears in relation to the Robertson–Seymour
Orders_of_magnitude_(numbers)
Function type in category theory
definition of lookup constructs to implement such “strong” functions like the Ackermann function. Algebras for a monad Algebraic data type Catamorphism Dialgebra
F-algebra
Fundamental combinatorial result of Ramsey theory
tic-tac-toe) the H given by the above argument grows as fast as the Ackermann function. The first primitive recursive bound is due to Saharon Shelah, and
Hales–Jewett_theorem
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Sorting algorithm
n ) {\displaystyle f(n)=A(n,n)} , where A {\displaystyle A} is Ackermann's function). Therefore, to sort a list arbitrarily badly, one would execute
Bogosort
Impossible task in computing
[ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an inputted statement
Entscheidungsproblem
Mathematical-logic system based on functions
as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped
Lambda_calculus
Certain large countable ordinal
In mathematics, the Ackermann ordinal is a certain large countable ordinal, named after Wilhelm Ackermann. The term "Ackermann ordinal" is also occasionally
Ackermann_ordinal
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
n))} where α ( m , n ) {\displaystyle \alpha (m,n)} is the inverse Ackermann function. Thus the total runtime of the algorithm is in O ( s o r t ( n ) +
Parallel algorithms for minimum spanning trees
Parallel_algorithms_for_minimum_spanning_trees
Intersection graph of a chord diagram
time. Their method is slower than linear by a factor of the inverse Ackermann function, and is based on lexicographic breadth-first search. The running time
Circle_graph
Axiomatic set theories based on the principles of mathematical constructivism
as the Ackermann function. The definition of the operator involves predicates over the naturals and so the theoretical analysis of functions and their
Constructive_set_theory
Geometric graph with unit edge lengths
β {\displaystyle \beta } is a very slowly growing function related to the inverse Ackermann function. This result leads to a similar bound on the number
Unit_distance_graph
Subdivision of the plane by lines
O(n\alpha (n))} , where α {\displaystyle \alpha } denotes the inverse Ackermann function, as may be shown using Davenport–Schinzel sequences. The sum of squares
Arrangement_of_lines
Turing machine that halts for any input
sophisticated functions always halt. For example, the Ackermann function, which is not primitive recursive, nevertheless is a total computable function computable
Decider_(Turing_machine)
Data structure that maintains info about the connected components of a graph
(\alpha (n))} , where n is the number of vertices and α is the inverse Ackermann function. The case in which edges can only be deleted was solved by Shimon
Dynamic_connectivity
Hungarian mathematician
woman to be elected to the Hungarian Academy of Sciences. Ackermann function Recursive function theory List of pioneers in computer science Morris & Harkleroad
Rózsa_Péter
Infinite cardinal number
defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"),
Aleph_number
Czech mathematician (born 1966)
(n)^{|u|-4})})} , where α ( n ) {\displaystyle \alpha (n)} denotes the inverse Ackermann function and | u | {\displaystyle |u|} is the length of u {\displaystyle u}
Martin_Klazar
Type of abstract computing machine
compute any primitive recursive function (e.g. multiplication) but not all mu recursive functions (e.g. the Ackermann function). Elgot–Robinson investigate
Register_machine
i , j ) {\displaystyle A(4i,j)} where A {\displaystyle A} is the Ackermann function. Experimentally, however, each subsequence appears much earlier in
Ehrenfeucht–Mycielski sequence
Ehrenfeucht–Mycielski_sequence
Mathematical function on ordinals
In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced
Veblen_function
the analysis of existence, uniqueness and their evaluation. The Ackermann functions and tetration can be interpreted in terms of superfunctions. Analysis
Superfunction
Church–Turing thesis Computable function Algorithm Recursion Primitive recursive function Mu operator Ackermann function Turing machine Halting problem
List of mathematical logic topics
List_of_mathematical_logic_topics
Target set of a mathematical function
mathematics, a codomain or set of destination of a function is a set into which all of the outputs of the function are constrained to fall. It is the set Y in
Codomain
Input to a mathematical function
of a function is a value provided to obtain the function's result. It is also called an independent variable. For example, the binary function f ( x
Argument_of_a_function
Mathematical operation with two operands
arity two. More specifically, a binary operation on a set is a binary function that maps every pair of elements of the set to an element of the set. Examples
Binary_operation
Type of mathematical function
many such schemes of ordinal notations, including schemes by Wilhelm Ackermann, Heinz Bachmann, Wilfried Buchholz, Georg Cantor, Solomon Feferman, Gerhard
Ordinal_notation
Mathematical function such that every output has at least one input
surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there
Surjective_function
Procedural extension for SQL and the Oracle relational database
simulate associative arrays, as in this example of a memo function for Ackermann's function in PL/SQL. With index-by tables, the array can be indexed
PL/SQL
Function returning one of only two values
switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the
Boolean_function
Process of repeating items in a self-similar way
where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values),
Recursion
Number of arguments required by a function
science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank,
Arity
Thesis on the nature of computability
in the 1930s was the Entscheidungsproblem of David Hilbert and Wilhelm Ackermann, which asked whether there was a mechanical procedure for separating mathematical
Church–Turing_thesis
Finite sets whose elements are all hereditarily finite sets
countable. In 1937, Wilhelm Ackermann introduced an encoding of hereditarily finite sets as natural numbers. It is defined by a function f : H ℵ 0 → ω {\displaystyle
Hereditarily_finite_set
Measure of algorithm performance for large inputs
{\displaystyle \alpha (n)} is the very slowly growing inverse of the Ackermann function, but the best known lower bound is the trivial Ω ( n ) {\displaystyle
Asymptotically optimal algorithm
Asymptotically_optimal_algorithm
Polygonal region of all points visible from a given point in a plane
vertices, where α ( n ) {\displaystyle \alpha (n)} is the inverse Ackermann function. A worst case optimal divide-and-conquer algorithm running in Θ (
Visibility_polygon
Axiomatization of arithmetic
discussed with potential function symbols added for primitive recursive functions. That theory proves the Ackermann function total. Beyond this, axiom
Heyting_arithmetic
Computing problem
{\displaystyle \alpha _{c}} is a certain functional inverse of the Ackermann function. There are some semigroup operators that admit slightly better solutions
Range query (computer science)
Range_query_(computer_science)
Function, homomorphism, or morphism
In mathematics, a map or mapping is a function in its general sense.[vague] These terms may have originated as from the process of making a geographical
Map_(mathematics)
Month of 1962
Award winner; in Brooklyn Died: Wilhelm Ackermann, 66, German mathematician known for the Ackermann function in the theory of computation The Niña II
December_1962
ACKERMANN FUNCTION
ACKERMANN FUNCTION
Boy/Male
American, British, English
Man of Oak
Biblical
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Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a great functionary.
Boy/Male
British, English
Shear Man
Surname or Lastname
Dutch
Dutch : occupational name from akkerman ‘plowman’; a frequent name in New Netherland in the 17th century. Later, it probably absorbed some cases of the cognate German and Swedish names, Ackermann and Åkerman respectively.English : from a medieval term denoting feudal status, Middle English akerman (Old English æcerman, from æcer ‘field, acre’ + man ‘man’). Typically, an ackerman was a bond tenant of a manor holding half a virgate of arable land, for which he paid by serving as a plowman. The term was also used generically to denote a plowman or husbandman.Variant of German and Jewish Ackermann.
Male
Egyptian
, Functionary of the Interior.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English (Somerset)
English (Somerset) : variant of Ackerman.Americanized spelling of Dutch Ackerman or German Ackermann.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, a high Egyptian functionary.
Male
Celtic
, great justiciary, or functionary.
ACKERMANN FUNCTION
ACKERMANN FUNCTION
Male
English
English and French form of Latin Paulus, PAUL means "small." In the bible, this is the name of the author of the 14 epistles of the New Testament.
Girl/Female
Spanish Greek Latin
Vigilant.
Boy/Male
Muslim
Name of place in saudi arabia
Boy/Male
Indian
Smart
Girl/Female
Arabic, Muslim, Sindhi
Daughter of Sayfi Al-ansari; She was a Companion
Boy/Male
Indian, Punjabi, Sikh
A Person of Good Family
Girl/Female
Tamil
Goddess Parvati
Boy/Male
Indian, Punjabi, Sikh
One who is Friendly with Charity
Boy/Male
Hindu, Indian, Sanskrit
Rama of the Moon
Boy/Male
Tamil
Rajasekar | ராஜஸேகரÂ
Lord Shiva, The highest of the rulers
ACKERMANN FUNCTION
ACKERMANN FUNCTION
ACKERMANN FUNCTION
ACKERMANN FUNCTION
ACKERMANN FUNCTION
v. i.
Alt. of Functionate
a.
Of, pertaining to, or designating, certain secret tribunals which flourished in Germany from the end of the 12th century to the middle of the 16th, usurping many of the functions of the government which were too weak to maintain law and order, and inspiring dread in all who came within their jurisdiction.
v. i.
To execute or perform a function; to transact one's regular or appointed business.
a.
Destitute of function, or of an appropriate organ. Darwin.
prep.
Acting as a substitute; -- said of abnormal action which replaces a suppressed normal function; as, vicarious hemorrhage replacing menstruation.
n.
Fig.: Any cavity, or hollow place, in which any function may be conceived of as operating.
a.
Having relation to growth or nutrition; partaking of simple growth and enlargement of the systems of nutrition, apart from the sensorial or distinctively animal functions; vegetal.
a.
Pertaining to, or connected with, a function or duty; official.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
a.
Pertaining to the function of an organ or part, or to the functions in general.
a.
Belonging or relating to life, either animal or vegetable; as, vital energies; vital functions; vital actions.
n.
The doctrine that all the functions of a living organism are due to an unknown vital principle distinct from all chemical and physical forces.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
pl.
of Functionary
n.
One deputed or authorized to perform the functions of another; a substitute in office; a deputy.
adv.
In a functional manner; as regards normal or appropriate activity.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Of or pertaining to the vessels of animal and vegetable bodies; as, the vascular functions.
v. t.
To assign to some function or office.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.