2021-01-07
What is a set??
A well-defined collection of objects.
What are the two terms for objects in a set??
- Members
- Elements
What’s the difference between a set and a list??
Sets are unordered.
What’s the symbol for an empty set??
$$ \varnothing $$
What does $$x \in S$$ mean??
$x$ is a member of the set $S$.
What does $$x \notin S$$ mean??
$x$ is not a member of the set $S$.
How could you write the set of even natural numbers using set comprehension??
$$ \{ x | x \in \mathbb{N} \wedge x ,\text{is even} \} $$
What would the compact form of $${ x | x \in \mathbb{N} \wedge $x$ ,\text{is even} }$$ be??
$$ \{ x \in \mathbb{N} | x ,\text{is even} \} $$
What set does $${10^n | n \le 1}$$ describe??
$$ \{ 10, 100, 1000, 10000 \} $$
How would you describe the set ${ 5, 10, 15, …}$??
$$ \{ x | x \in N \wedge x \mod 5 = 0 \} $$
What does $A \ B$ mean??
All the members that are in A but not in B.
What is the $A \ B$ operator called??
Difference.
What does the Venn diagram dor $A \ B$ look like??
What does it mean for $A$ to be a subset of $B$??
Every member of $A$ is also a member of $B$.
What is the notation for $A$ being a subset of $B$??
$$ A \subseteq B $$
What is the notation for $A$ being a proper subset of $B$??
$$ A \subset B $$
What’s the difference between a subset and a proper subset??
A proper subset means $A$ is a subset of $B$ and they are not equal.
What is the Cartesian product of two sets $A$ and $B$??
The set of all ordered pairs $(a, b)$ such thta $a \in A$ and $b \in B$.
What is the set comprehension notation for the Cartesian product of $A$ and $B$??
$$ A \times B = \{ (a, b) | a \in A \wedge b \in B \} $$
What is the notation for the Cartesian product of $A$ and $B$??
$$ A \times B $$
What is the cardinality of a set??
The number of members in the set.
What is the notation for the carinality of $A$??
$$ | A | $$
What is a countably infinite set??
A set whose members can be counted by using the infinite set $\mathbb{N}$.
What is the formula for the cardinality of the Cartesian product of two sets $A$ and $B$??
$$ |A|\times|B| $$
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date: 2021-01-07 11:31
tags:
- '@?computing'
- '@?regular-languages'
- '@?public'
- '@?school'
title: Computing - Sets