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Abstract Algebra

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Cardinality of a Set: definition and examples

ABSALG-YS3ENQ

The cardinality of a set $S$ is the number of elements in $S$.

Common notations for the cardinality of a set $S$ are ${\rm Card}(S)$, and $|S|$.

We use $|S|$.

An infinite set $S$ has cardinality $|S|=\infty$.

The empty set $S=\emptyset$ is the set with no elements and $|\emptyset|=0$.

Which of the following $S$ sets has $|S|=7$? (Select all that apply.)

A

$S=\{x$ prime number $\mid$ 1<x<19$\}$

B

$S=\{$ Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday$\}$

C

$S=\{x\in{\mathbb Z}\mid\, x$ odd, 5< x< 9$\}$

D

$S=\{x\in{\mathbb Z} \mid x=3k+4, \; k\in{\mathbb Z}\}$

E

$S=\{x\in{\mathbb R}\mid\,1\le x\le 7\}$