140 lines
4.1 KiB
Markdown
140 lines
4.1 KiB
Markdown
---
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title: Set
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TARGET DECK: Obsidian::STEM
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FILE TAGS: set
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tags:
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- set
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---
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## Overview
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%%ANKI
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Basic
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How does Knuth define a *dynamic* set?
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Back: As a set that can change over time.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070055-->
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END%%
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%%ANKI
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Basic
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How does Knuth distinguish mathematical sets from dynamic sets?
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Back: The former is assumed to be unchanging.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070059-->
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END%%
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%%ANKI
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Basic
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How does Knuth define a dictionary?
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Back: As a dynamic set that allows insertions, deletions, and membership tests.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070063-->
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END%%
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%%ANKI
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Basic
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Which of dynamic sets and dictionaries are more general?
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Back: The dynamic set.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070067-->
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END%%
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%%ANKI
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Basic
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Is a dynamic set a dictionary?
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Back: Not necessarily.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070071-->
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END%%
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%%ANKI
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Basic
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Is a dictionary a dynamic set?
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Back: Yes.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070077-->
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END%%
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%%ANKI
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Cloze
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A dictionary supports {insertions}, {deletions}, and {membership testing}.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Tags: adt::dynamic_set
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<!--ID: 1715432070083-->
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END%%
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%%ANKI
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Basic
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Define the set of prime numbers less than $10$ using abstraction.
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Back: $\{x \mid x < 10 \land x \text{ is prime}\}$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028616-->
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END%%
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%%ANKI
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Basic
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Define the set of prime numbers less than $5$ using set-builder notation.
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Back: $\{x \mid x < 5 \land x \text{ is prime}\}$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028645-->
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END%%
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%%ANKI
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Basic
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Define the set of prime numbers less than $5$ using roster notation.
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Back: $\{2, 3\}$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028649-->
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END%%
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%%ANKI
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Basic
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Define the set of prime numbers less than $5$ using abstraction.
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Back: $\{x \mid x < 5 \land x \text{ is prime}\}$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028652-->
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END%%
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%%ANKI
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Basic
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What term describes the expression to the right of $\mid$ in set-builder notation?
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Back: The entrance requirement.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028656-->
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END%%
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%%ANKI
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Basic
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What term refers to $\_\_\; x\; \_\_$ in $\{x \mid \_\_\; x\; \_\_\}$?
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Back: The entrance requirement.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028659-->
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END%%
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%%ANKI
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Basic
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The term "entrance requirement" refers to what kind of set notation?
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Back: Set-builder/abstraction.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028663-->
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END%%
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%%ANKI
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Basic
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What name is given to set notation in which members are explicitly listed?
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Back: Roster notation.
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1715786028667-->
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END%%
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## Bibliography
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* Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022). |