notebook/notes/set/index.md

title	TARGET DECK	FILE TAGS	tags
Set	Obsidian::STEM	set	set

Overview

%%ANKI Basic How does Knuth define a dynamic set? Back: As a set that can change over time. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic How does Knuth distinguish mathematical sets from dynamic sets? Back: The former is assumed to be unchanging. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic How does Knuth define a dictionary? Back: As a dynamic set that allows insertions, deletions, and membership tests. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic Which of dynamic sets and dictionaries are more general? Back: The dynamic set. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic Is a dynamic set a dictionary? Back: Not necessarily. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic Is a dictionary a dynamic set? Back: Yes. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Cloze A dictionary supports {insertions}, {deletions}, and {membership testing}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). Tags: adt::dynamic_set

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%%ANKI Basic Define the set of prime numbers less than 10 using abstraction. Back: \{x \mid x < 10 \land x \text{ is prime}\} Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Define the set of prime numbers less than 5 using set-builder notation. Back: \{x \mid x < 5 \land x \text{ is prime}\} Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Define the set of prime numbers less than 5 using roster notation. Back: \{2, 3\} Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Define the set of prime numbers less than 5 using abstraction. Back: \{x \mid x < 5 \land x \text{ is prime}\} Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What term describes the expression to the right of \mid in set-builder notation? Back: The entrance requirement. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What term refers to \_\_\; x\; \_\_ in \{x \mid \_\_\; x\; \_\_\}? Back: The entrance requirement. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic The term "entrance requirement" refers to what kind of set notation? Back: Set-builder/abstraction. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What name is given to set notation in which members are explicitly listed? Back: Roster notation. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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Classes

The Zermelo-Fraenkel alternative avoids speaking of collections defined using set theoretical notation that are not sets. The von Neumann-Bernays alternative calls these classes.

%%ANKI Basic In set theory, what is a class? Back: A collection defined using set theoretical notation that isn't a set. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Which two alternatives are usually employed when speaking of classes? Back: The Zermelo-Fraenkel alternative and the von Neumann-Bernays alternative. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What does the Zermelo-Fraenkel alternative say about classes? Back: It gives it no ontological status at all. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What does the von Neumann-Bernays alternative say about classes? Back: It refers to objects defined using set theory but that aren't actually sets. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Cloze The {1:Zermelo}-{2:Fraenkel} alternative is a separate approach from the {2:von Neumann}-{1:Bernays} alternative. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Which set theory alternative avoids the term "class"? Back: The Zermelo-Fraenkel alternative. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Which set theory alternative embraces the term "class"? Back: The von Neumann-Bernays alternative. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What kind of mathematical object is \{x \mid x \neq x\}? Back: A set. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What name is given to \{x \mid x \neq x\}? Back: The empty set. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What kind of mathematical object is \{x \mid x = x\}? Back: A class. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic What name is given to \{x \mid x = x\}? Back: The class of all sets. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Are sets or classes more general? Back: Classes. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Is every set a class? Back: Yes. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Is every class a set? Back: No. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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%%ANKI Basic Assuming entrance requirement \_\_\_, what kind of mathematical object is \{x \mid \_\_\_\}? Back: A class. Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).

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Bibliography

• Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
• Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).