Set Cardinality

The cardinality of a set is the number of elements that the set has, i.e., the size of the set. For a set $S$, we denote its cardinality as $|S|$ (

$|S|$

). Examples:

• For $S = \{😀, 😁, 😎, 😜\}$, we have $|S| = 4$.
• For $N = \{1, 2, \dots, 100\}$, we have $|N| = 100$.
• For $I = \{1, 2, 3, \dots\}$, we have $|I| = \infty$ (

  $\infty$

  ).

While the cardinality of a finite set is a fixed, nonnegative integer, this of an infinite set is infinity. There are actually different types of infinity, such as countable and uncountable; you'll learn more on those in more advanced CS courses.

Fun Class Activity: What is each of the following equal to?

1. $|\mathbb{Z}|$
2. $|\{2n\ |\ 0 \le n \le 5\}|$
3. $|\emptyset|$