# 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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1. With mutually exclusive conflicting desires from their candidate of, choice , Ambiguity is a powerful tool of political science. More problematic are words
2. 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
3. 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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. 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
15. Ambiguity is contrasted with semantic ambiguity. The former represents a, choice ,between a finite number of known and meaningful context-dependent
16. 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
17. 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
18. 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
19. 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
20. And thus deliberation),and only humans are capable of deliberation and, choice , " What is not capable of action cannot do anything by chance ". Metaphysics
21. Corrupt alternatives. Punishment According to Schopenhauer, whenever we make a, choice ," we assume as necessary that that decision was preceded by something from
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. Known and meaningful context-dependent interpretations. The latter represents a, choice ,between any number of possible interpretations, none of which may have a
32. 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 ".
33. 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
34. 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
35. 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
36. 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
37. And Thai (an abused). In Thai, tone is determined primarily by the, choice ,of consonant, with diacritics for disambiguation. In the Pollard script, an
38. 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
39. 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
40. Position argues that a woman has certain reproductive rights, especially the, choice ,whether to carry a pregnancy to term. Modern abortion law Current laws
41. Mathematical results, such as Tychonoff's theorem, require the axiom of, choice ,for their proofs. Contemporary set theorists also study axioms that are not
42. 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
43. 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.
44. 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
45. Drawing from Austrian School economics, study of law and economics and public, choice ,theory, while the burgeoning feminist and environmentalist movements also
46. 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
47. 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
48. 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
49. 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
50. 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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