Cardinal
Concept history
A revision trail for this concept page.
Revision 2241
8/24/2026, 10:30:15 AM · Sequoia
Shared settings updated from fr translation
linked exercisesNoneCardinal = nombre d’éléments ?, Cardinal de
Revision 2236
8/24/2026, 10:25:56 AM · Sequoia
Concept marked usable
statusStubUsable
Revision 2235
8/24/2026, 10:25:51 AM · Sequoia
Updated text
Compare with revision 35912 changed lines
1
The cardinal of a [[Set|set]] $E$ is the number of elements in $E$.1
#### Intuitive definition2
The cardinal of a finite [[Set|set]] $E$ is the number of elements in $E$. It is often denoted as $\vert E\vert$ or $\#E$ or also $\mathrm{Card}(E)$.2
3
More formally... I have no clue how it's defined. Something utterly deranged if I had to guess.4
#### Formal definition5
6
More formally, the cardinal of a set $E$ is the smallest integer $n$ such that there exists an injection from $E$ to $[\![1,n]\!]$. If it does not exists, we set $\vert E\vert=+\infty$.7
8
#### Examples9
$\bullet$ The set $\{1,8,36\}$ has $3$ elements, hence $\vert \{1,8,36\}\vert=3$.10
$\bullet$ The set $\{(1,2), \text{Anna}, \pi^2, \{1\}\}$ has $4$ elements, hence its cardinal is $4$.11
$\bullet$ There is an infinite number of integers, so $\vert \Z\vert=+\infty$.Revision 359
7/8/2026, 6:56:14 PM · Ancient Tree
Concept created
The cardinal of a [[Set|set]] $E$ is the number of elements in $E$. More formally... I have no clue how it's defined. Something utterly deranged if I had to guess.