Examples of the the word, choice , in a Sentence Context
The word ( choice ), is the 706 most frequently used in English word vocabulary
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- With mutually exclusive conflicting desires from their candidate of, choice , Ambiguity is a powerful tool of political science. More problematic are words
- To the subproblems do not have to be known at each stage; instead a" greedy ", choice ,can be made of what looks best for the moment. The greedy method extends the
- The use of Loyalists presented the British with" major problems of strategic, choice ," since while it was necessary to widely disperse troops in order to defend
- Infinite, and thus implies that every finite collection of nonempty sets has a, choice ,function. However, that particular case is a theorem of Carmelo–Frankel set
- One variation avoids the use of choice functions by, in effect, replacing each, choice ,function with its range.: Given any set X of pairwise disjoint non-empty sets
- Should then be fixed to the tops of the walls using the builder’s preferred, choice ,of attachments. Taking into account the material from which the beams and walls
- In the presence of other basic axioms of set theory, they imply the axiom of, choice ,and are implied by it. One variation avoids the use of choice functions by, in
- Function, the axiom of choice can be compactly stated as: Every set has a, choice ,function. Which is equivalent to: For any set A there is a function f such that
- Sets:: For any set A, the power set of A (with the empty set removed) has a, choice ,function. Authors who use this formulation often speak of the choice function
- With the axiom of choice , such as the axiom of determinant. Unlike the axiom of, choice , these alternatives are not ordinarily proposed as axioms for mathematics, but
- Of the Cartesian product of all distinct sets in the family. The axiom of, choice ,asserts the existence of such elements; it is therefore equivalent to:: Given
- To arbitrary collections. Usage Until the late 19th century, the axiom of, choice ,was often used implicitly, although it had not yet been formally stated. For
- Mathematical induction. In the even simpler case of a collection of one set,a, choice ,function just corresponds to an element, so this instance of the axiom of
- And so only makes sense for sets of sets. With this alternate notion of, choice ,function, the axiom of choice can be compactly stated as: Every set has a
- Ambiguity is contrasted with semantic ambiguity. The former represents a, choice ,between a finite number of known and meaningful context-dependent
- That there exists a set of nonempty sets which has no choice function. Each, choice ,function on a collection X of nonempty sets is an element of the Cartesian
- For sets of sets. With this alternate notion of choice function, the axiom of, choice ,can be compactly stated as: Every set has a choice function. Which is
- Has a choice function. Authors who use this formulation often speak of the, choice ,function on A, but be advised that this is a slightly different notion of
- Function on A, but be advised that this is a slightly different notion of, choice ,function. Its domain is the power set of A (with the empty set removed),and
- And thus deliberation),and only humans are capable of deliberation and, choice , " What is not capable of action cannot do anything by chance ". Metaphysics
- Corrupt alternatives. Punishment According to Schopenhauer, whenever we make a, choice ," we assume as necessary that that decision was preceded by something from
- Set. Variants There are many other equivalent statements of the axiom of, choice , These are equivalent in the sense that, in the presence of other basic axioms
- A, whereas with the definition used elsewhere in this article, the domain of a, choice ,function on a collection of sets is that collection, and so only makes sense
- But only as principles in set theory with interesting consequences. Statement A, choice ,function is a function f, defined on a collection X of nonempty sets, such that
- In law, finance and economics and hospitality and tourism management. Since the, choice ,for higher education on the island itself is limited, many students choose
- Axiom of choice states that there exists a set of nonempty sets which has no, choice ,function. Each choice function on a collection X of nonempty sets is an element
- The respondent's life was. Rand's Atlas Shrugged was the second most popular, choice , after the Bible. Rand's books continue to be widely sold and read, with 25
- Case is a theorem of Carmelo–Frankel set theory without the axiom of, choice ,(ZF); it is easily proved by mathematical induction. In the even simpler case
- The axiom can be stated:: For any set X of nonempty sets, there exists a, choice ,function f defined on X. Thus the negation of the axiom of choice states that
- The axiom of choice and are implied by it. One variation avoids the use of, choice ,functions by, in effect, replacing each choice function with its range.: Given
- Known and meaningful context-dependent interpretations. The latter represents a, choice ,between any number of possible interpretations, none of which may have a
- Theory on abstract instead of concrete machines, arbitrariness of the, choice ,of a model remains. It is at this point that the notion of simulation enters ".
- It is in the sphere of moral actions. According to Aristotle, luck must involve, choice ,(and thus deliberation),and only humans are capable of deliberation and
- In others, it resulted in money being donated to a charity of the volunteer's, choice , During these activities, the researchers took functional magnetic resonance
- Of elements with x_i \in S_i for every i \in I. Informally put, the axiom of, choice ,says that given any collection of bins, each containing at least one object, it
- Features),such a selection can be obtained only by invoking the axiom of, choice , The axiom of choice was formulated in 1904 by Ernst Carmelo. Although
- And Thai (an abused). In Thai, tone is determined primarily by the, choice ,of consonant, with diacritics for disambiguation. In the Pollard script, an
- Set theorists also study axioms that are not compatible with the axiom of, choice , such as the axiom of determinant. Unlike the axiom of choice , these
- X. " In general, it is impossible to prove that F exists without the axiom of, choice , but this seems to have gone unnoticed until Carmelo. Not every situation
- Position argues that a woman has certain reproductive rights, especially the, choice ,whether to carry a pregnancy to term. Modern abortion law Current laws
- Mathematical results, such as Tychonoff's theorem, require the axiom of, choice ,for their proofs. Contemporary set theorists also study axioms that are not
- Says that every nonempty set has an element; this holds trivially. The axiom of, choice ,can be seen as asserting the generalization of this property, already evident
- Exists a choice function f defined on X. Thus the negation of the axiom of, choice ,states that there exists a set of nonempty sets which has no choice function.
- B) does not lie in B. Restriction to finite sets The statement of the axiom of, choice ,does not specify whether the collection of nonempty sets is finite or infinite
- Drawing from Austrian School economics, study of law and economics and public, choice ,theory, while the burgeoning feminist and environmentalist movements also
- To fill the late Chief Justice Taney's seat on the Supreme Court, he named the, choice ,of the Radicals, Salmon P. Chase, who Lincoln believed would uphold the
- Similarities in the language. Regional dialects In mathematics, the axiom of, choice , or AC, is an axiom of set theory stating that for every family (S_i)_ of
- Function just corresponds to an element, so this instance of the axiom of, choice ,says that every nonempty set has an element; this holds trivially. The axiom of
- Bin. In many cases such a selection can be made without invoking the axiom of, choice ,; this is in particular the case if the number of bins is finite, or if a
- A selection can be obtained only by invoking the axiom of choice . The axiom of, choice ,was formulated in 1904 by Ernst Carmelo. Although originally controversial, it
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