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notebook/notes/set/bags.md

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title TARGET DECK FILE TAGS tags
Bags Obsidian::STEM set::bag
bag
set

Overview

Sets can contain the same element only once. This means \{1, 1\} = \{1\}. A bag (or multiset) can include a single element multiple times.

%%ANKI Basic What is a bag? Back: A set in which we are allowed to include a single element multiple times. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What alternative term do "bags" go by? Back: Multisets. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Cloze The {multiplicity} of an element in a bag is the {number of instances given for that element}. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic How many bags exist with members a and b? Back: An infinite amount. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What is the multiplicity of a in bag \{a, b\}? Back: 1 Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What is the multiplicity of a in bag \{a, a, a, b, b, c\}? Back: 3 Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What distinguishes a bag from a tuple? Back: Order is irrelevant in the former. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What is the cardinality of a in bag \{a, a, a, b, b, c\}? Back: N/A. Cardinality applies to bags, not members. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic What is the cardinality of bag \{a, a, a, b, b, c\}? Back: 6 Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic How is the cardinality of a bag calculated? Back: By summing the multiplicities of each member. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic When viewed as a function, a multiset has domain what? Back: The set comprising each member of the multiset. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic When viewed as a function, a multiset has range what? Back: The set comprising the multiplicities of the multiset's members. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic When viewed as a function, a multiset has codomain what? Back: The positive integers. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic Do all multisets correspond to sets? Back: No. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic Do all sets correspond to multisets? Back: Yes. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

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%%ANKI Basic Under what condition is a bag also a set? Back: When the multiplicity of each element in the bag is 1. Reference: “Multiset,” in Wikipedia, April 4, 2024, https://en.wikipedia.org/w/index.php?title=Multiset&oldid=1217165725.

END%%

Bibliography