--- title: Set TARGET DECK: Obsidian::STEM FILE TAGS: set tags: - 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 END%% %%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 END%% %%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 END%% %%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 END%% %%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 END%% %%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 END%% %%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 END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% ## 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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%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). END%% %%ANKI Basic Are sets or classes more general? Back: Classes. Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). END%% %%ANKI Basic Is every set a class? Back: Yes. Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). END%% %%ANKI Basic Is every class a set? Back: No. Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977). END%% %%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). END%% ## 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).