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Topic: Choice function

	Choice function - Wikipedia, the free encyclopedia
		A choice function is a mathematical function f whose domain X is a collection of nonempty sets such that for every S in X, f(S) is in S.
		A weaker form of axiom of Choice, the axiom of countable choice (CC) states that every countable set of nonempty sets has a choice function.
		If S is a finite set of nonempty sets, then one can construct a choice function for S by picking one element from each member of S.
	en.wikipedia.org /wiki/Choice_function (374 words)

	PlanetMath: axiom of choice
		, the axiom of choice is unnecessary to prove the existence of a choice function.
		Thus objects that are proved to exist using the axiom of choice cannot generally be described by any kind of systematic rule, for if they could it would not be necessary to their construction.
		This is version 12 of axiom of choice, born on 2001-10-18, modified 2005-07-20.
	planetmath.org /encyclopedia/AxiomOfChoice.html (639 words)

	System and method for providing an adaptive dialog function choice model for various communication devices - Patent ...
		The system of claim 43, wherein said function navigation structure establishes limits on movement between said function choices with respect to a first type of user device which are different than limits on movement between said function choices with respect to a second type of user device.
		The method of claim 52, wherein said function navigation structure establishes limits on movement between said function choices with respect to a first type of user device which are different than limits on movement between said function choices with respect to a second type of user device.
		Function 11 may be a checking account menu; function 12 may be a credit card account menu; and another function may be a loan application function.
	www.freepatentsonline.com /6246989.html (6413 words)

	CHOICE LISTS Function (Site not responding. Last check: 2007-10-13)
		Choice lists are a way of collecting hierarchical information and assembling them into a string of codes and a string of text descriptions.
		On advantage of performing the choice list routine in custom code is that you can pass additional information to the routine and cause choice list processing to start in the middle of a choice list table.
		If the choice list was invoked from the "General Before" section, and the user "Aborts/rejects" the choice list, the current value in the _CL field is not changed.
	www.rollcim.com /documentation/optutil500_web/CHOICE_LISTS_FM.HTML (1042 words)

	PlanetMath: choice function
		The Axiom of Choice (AC) states that every set of nonempty sets does have a choice function.
		In this case we may be making infinitely many choices, but we have a rule for making the choices, so AC is not needed.
		This is version 7 of choice function, born on 2004-10-25, modified 2005-06-25.
	planetmath.org /encyclopedia/ChoiceFunction.html (304 words)

	Choice---Lecture Notes (Site not responding. Last check: 2007-10-13)
		In the case of a choice function, the domain is the set of all subsets of A; the range is also the set of all subsets of A.
		We often observe the choices of a given person or group over time, and for one reason or another ask whether the observed pattern of choices meets, or can be expected to meet, criteria of coherence or acceptability.
		On the presumption that choice over a very large set of alternatives, having a strong property similarity of ``nearby'' alteratives, we treat such choice as though it were over a genuinely continuous set.
	www.artsci.wustl.edu /~polisci/calvert/PolSci5052/choice.html (3127 words)

	Choice as a function of reinforcement ratios in delayed matching to sample. (Site not responding. Last check: 2007-10-13)
		Choice as a function of reinforcement ratios in delayed matching to sample.
		Hartl, J. A., and Fantino, E. Choice as a function of reinforcement ratios in delayed matching to sample.
		In Experiment 2, 4 subjects were exposed to a delayed matching-to-sample task in which the retention intervals and the reduction in delay to reinforcement signaled by the onset of the sample stimulus were independently varied.
	seab.envmed.rochester.edu /abstracts/JeabAbstracts/66/%2066-011.Htm (288 words)

	Axiom of choice Article, Axiomchoice Information (Site not responding. Last check: 2007-10-13)
		The axiom of choice has been proven to be independent of the remaining axioms of set theory ; that is, it can be neither proven nor disproven from them (unless those remaining axioms contain anunknown contradiction).
		An example of this is the Banach-Tarski paradox which amounts to saying that it is possible to "carve-up" the 3-dimensionalsolid unit ball into finitely many pieces, and, using only rotation and translation, reassemble the pieces into two balls eachwith the same volume as the original.
		Several central theorems in various branches of mathematics require the axiom of choice (or one of its weaker versions, suchas the Boolean prime ideal theorem, the axiom of countable choice, or the axiom of dependent choice).
	www.anoca.org /set/sets/axiom_of_choice.html (995 words)

	CHOICE FUNCTION
		The axiom of choice has been proven to be independent of the remaining axioms of set theory; that is, it can be neither proven nor disproven from them (unless those remaining axioms contain a contradiction, which we don't know).
		One of the most interesting aspects of the axiom of choice is the sheer number of places in mathematics that it shows up.
		Several central theorems in various branches of mathematics require the axiom of choice (or one of its weaker versions, such as the ultrafilter lemma, the axiom of countable choice, or the axiom of dependent choice).
	www.websters-online-dictionary.org /definition/CHOICE+FUNCTION (1060 words)

	Axiom of Choice (Site not responding. Last check: 2007-10-13)
		The Axiom of Choice (AC) was formulated about a century ago, and it was controversial for a few of decades after that; it may be considered the last great controversy of mathematics.
		In effect, when we accept the Axiom of Choice, this means we are agreeing to the convention that we shall permit ourselves to use a choice function f in proofs, as though it "exists" in some sense, even though we cannot give an explicit example of it or an explicit algorithm for it.
		Consequences of the Axiom of Choice is a book by Paul Howard and Jean E. Rubin that was published by the American Mathematical Society in 1998.
	math.vanderbilt.edu /~schectex/ccc/choice.html (3626 words)

	Semantic Universals and Choice Function Theory (ResearchIndex) (Site not responding. Last check: 2007-10-13)
		One of conceptual problems for a theory with choice functions is that, even given that the semantics of indefinites involves functions, it still does not follow that these have to be choice functions.
		However, a so-far open question is whether there is any way to derive choice function interpretation from more general properties of natural language.
		Choice Functions and the Scopal Semantics of Indefinites - Winter (1997)
	citeseer.ist.psu.edu /12548.html (301 words)

	The Epsilon Calculus
		In his Hamburg lecture in 1921 (1922), Hilbert first presented the idea of using choice functions to deal with the principle of the excluded middle in a formal system for arithmetic.
		Reading the epsilon operator as an indefinite choice operator ("an x such that A(x)") suggests that it might be a useful tool in the analysis of indefinite and definite noun phrases in formal semantics.
		‘Choice functions and the scopal semantics of indefinites’.
	plato.stanford.edu /entries/epsilon-calculus (6438 words)

	Axiom of Choice - Computing Reference - eLook.org (Site not responding. Last check: 2007-10-13)
		Function f is a "choice function" for X - for each x in X, it chooses an element of x.
		We can also construct a choice function for most simple infinite sets of sets if they are generated in some regular way.
		However, there are some infinite sets for which the construction or specification of such a choice function would never end because we would have to consider an infinite number of separate cases.
	www.elook.org /computing/axiom-of-choice.htm (446 words)

	Calling C from Prolog
		Since the original term is passed to the function it is possible to read its value or to unify it.
		, the function shall return the address of a Prolog predicate and, at the exit of the function, the control is given to that predicate.
		is specified the string passed to the function is the internal string of the corresponding atom and should not be modified.
	www.csci.csusb.edu /dick/cs320/prolog/gnu/manual064.html (1488 words)

	A First Look at Graphical User Interfaces (Site not responding. Last check: 2007-10-13)
		Examples include buttons, which the user can click with the mouse and which trigger a function application; choice menus, from which the user can choose one of a collection of values; text fields, into which the user can type arbitrary text; and message fields, into which a program can draw text.
		The function that goes with a button is a function of one argument: an event.
		The result of the model function, in turn, is drawn into a message field, possibly after converting it to a string first.
	www.htdp.org /2001-09-22/Book/node121.htm (1851 words)

	[No title]
		For many sets, including any finite set, the first six axioms of set theory (abbreviated ZF) are enough to guarantee the existence of a choice function but there do exist sets for which AC is required to show the existence of a choice function.
		Since AC gives no method for constructing a choice set constructivists belong to school C. A formalist believes that mathematics is strictly symbol manipulation and any consistent theory is reasonable to study.
		For a formalist the notion of truth is confined to the context of a mathematical model, e.g., a formalist would say "The parallel postulate is false in Riemannian geometry." but she wouldn't say "The parallel postulate is false." A formalist will probably not align herself with any school.
	www.halcyon.com /pub/ii/math/ac/acfaq (1408 words)

	M3000 Homework #23 (Site not responding. Last check: 2007-10-13)
		(f) The Axiom of Choice is not needed, since A is a non-empty set of natural numbers, there is a smallest element of A and a choice function can be defined by choosing the smallest element of each set.
		In the first case, by definition, there is a one-to-one function from A to B. In the second case, there is a one-to-one function from B to A, call it f.
		is a partial function from a subset of A to B which is onto B. We can extend this partial function to a function from A to B by defining g: A
	www-math.cudenver.edu /~wcherowi/courses/m3000/abhw23.html (319 words)

	[No title]
		The argument in the function is array seats, it is passed by // reference.
		No // arguments in this function, The return character('1' '2' or '3') is // used in the while loop, which is the next step of the main function.
		In case1: first, call function // get_section() to get the section where the user wishes to reverse; then // call the function get_seat to find the first available seat in the section, // the return value of get_seat function is the index in the array seats[].
	www.pcs.cnu.edu /~szhang/CPSC230/my_airplane_C.txt (1357 words)

	CHOICE LISTS Function (Site not responding. Last check: 2007-10-13)
		On advantage of performing the choice list routine in custom code is that you can pass additional information to the routine and cause choice list procesing to start in the middle of a choice list table.
		This text will then be added to the end of the choice description create dy the choice list process.
		A value of "" means that the first choice* selection is required and that the user must select one of the valid choices.
	www.rollcim.com /ae500/CHOICE_LISTS_FM.HTML (1641 words)

	Chapter 4 Notes (Site not responding. Last check: 2007-10-13)
		The general rule is if the objective function measures a benefit, the decision maker seeks to maximize this benefit and is solving a maximization problem.
		The objective function is the total benefit function and the constraint is the total cost function.
		While the manager has access to various combinations of inputs, he or she must choose among these inputs to produce the exact quantity which is the constraint.
	www.gardner-webb.edu /intra/negbenebor/chapter4.htm (1166 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		I have included a non-member function scanfunction() that takes an ofstream and a randfunc object and outputs a thorough sample of data points from the function which can be used for graphing.
		Notice that choices 2 and 3 take a vector of theta and a single alpha, while choice 4 and 5 takes a vector of theta and a vector of alpha.
		The correlation function must accept two equal length vectors as input, and the double parameter is used for output of the result.
	www.cs.wm.edu /~va/software/krigifier/krigify.h (1980 words)

	Choice function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-13)
		Choice function -- Facts, Info, and Encyclopedia article
		A choice function is a (A mathematical relation such that each element of one set is associated with at least one element of another set) mathematical function whose domain is a collection of nonempty sets such that for every in, is in.
		The (additional info and facts about Axiom of Choice) Axiom of Choice is often stated in terms of a choice function: "For every collection of nonempty sets, there exists a choice function on."
	www.absoluteastronomy.com /encyclopedia/C/Ch/Choice_function.htm (94 words)

	Cahier 2001-01 (SMEALSearch) - Pal,Rangaswamy,Giles,Debnath (Site not responding. Last check: 2007-10-13)
		A selection function is a generalization of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options.
		A selection function is non-deteriorating if there exists an ordering over the universal set of alternatives such that the selected alternatives are at least as good as the reference option.
		We characterize non-deteriorating selection functions in an abstract framework and in an economic environment.
	smealsearch.psu.edu /10011.html (227 words)

	713 MIDTERM EXAM---SPRING 1997 (Site not responding. Last check: 2007-10-13)
		Prove that if a choice function has a utility representation then it has a complete and transitive binary representation.
		Prove algebraically that the indirect utility function is quasi-convex.
		Prove that if a choice function is representable by a complete, transitive, continuous, and monotone binary relation, then it has a utility representation.
	american.edu /academic.depts/cas/econ/faculty/isaac/exams/97s713m.htm (354 words)

	[No title]
		// //This function is a recursive function which gets the index of the first //occurance of a letter of a hidden word.
		If the letter is not a member of //the word, function returns -1.
		// //This function is a recursive function which finds the number of times a //letter appears in a hidden word.
	www.pcs.cnu.edu /~szhang/CPSC230/member_recursion_C.txt (452 words)

	J!NX Forums - CMD - Choice Function
		If you did any programming, just think of choice as a procedure.
		To use it, you do Call :Choice choices> and it sets %Choice.Answer% to whatever they answered.
		The funny thing about this signiture is that once you have finished reading it, you realise what a waste of time it has been.
	www.jinx.com /forum/topic.asp?TOPIC_ID=33628 (210 words)

	Existence of a Coalitionally Strategyproof Social Choice Function: A Constructive Proof ewp-pe/9604002 (Site not responding. Last check: 2007-10-13)
		This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies.
		The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is gdescribable.h The gdescribableh coalitions are assumed to form a countable Boolean algebra.
		The paper discusses oligarchical characteristics of the function, employing a specific interpretation of an infinite society.
	econwpa.wustl.edu /eprints/pe/papers/9604/9604002.abs (284 words)

	A Note On The Sum Of Differences Choice Function (ResearchIndex) (Site not responding. Last check: 2007-10-13)
		Abstract: This note deals with the problem of choice functions based on fuzzy preference relations.
		We study a choice function based on the sum of the differences and show that it is the only one to satisfy a system of three independent properties.
		A Note On The `Min In Favor' Choice Procedure For Fuzzy..
	citeseer.ist.psu.edu /662299.html (304 words)

	Manchester function rooms and function suites at The Willows. THE choice for function rooms in Manchester. (Site not responding. Last check: 2007-10-13)
		Manchester function rooms and function suites at The Willows.
		The Willows function rooms offer the best party atmosphere for your celebrations anywhere in the Manchester and the North West.
		With a range of function suites to choose from, we're sure you will find the suite that's just right for your party.
	www.thewillowsonline.co.uk /manchester-function-rooms.html (218 words)

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