nullndr/website
1
1
Fork 0
Code Issues Pull Requests Packages Projects Releases Activity

typos

Browse Source
This commit is contained in:
Andrea
2025-10-09 11:43:21 +02:00
parent 103ea91817
commit a1376991f5
1 changed files with 7 additions and 7 deletions
Download Patch File Download Diff File Expand all files Collapse all files

14
content/set_theory.md
View File

@@ -37,7 +37,7 @@ Two special sets are defined: the [[empty set|#empty-set]] and the [[universe se
### Empty set
The empty set, denotated with $\\{\\}$ or with the $\varnothing$ symbol, is a special set that has no element.
The empty set, denoted with $\\{\\}$ or with the $\varnothing$ symbol, is a special set that has no element.
### Universe set
@@ -47,7 +47,7 @@ The universal set, denoted by $U$, is a set that has as elements all unique elem
Before going further inside the set theory, it is worth introducing the notations for them.
Sets are typically denotated by an italic capital letter, like $A$, $B$, $C$ etc.
Sets are typically denoted by an italic capital letter, like $A$, $B$, $C$ etc.
To list the elements of a given set the enumeration notation is used. This list the elements of a set between curly braces. For example, to reppresent the set $A$ of all natural numbers less than 8 we write the following:
@@ -55,13 +55,13 @@ $$ A = \\{ 1, 2, 3, 4, 5, 6, 7 \\} $$
## Element membership
We denotate that an element is a member of a given set with the $\in$ symbol: given the previous set $A$, we write that
We denote that an element is a member of a given set with the $\in$ symbol: given the previous set $A$, we write that
$$ 1 \in A $$
This can be read as 1 is a member of set $A$, or 1 is inside set $A$.
The symbol $\notin$ is the opposite of the $\in$ symbol, it denotates an element that is not a member of a given set: given the previous set $A$, we write that
The symbol $\notin$ is the opposite of the $\in$ symbol, it denotes an element that is not a member of a given set: given the previous set $A$, we write that
$$ 8 \notin A $$
@@ -159,7 +159,7 @@ Just like algebra has his operations on numbers, sets have their own operations.
The union of two or more sets is a set that contains all elements in the given sets, with no duplicated element.
It's denotated with the $\cup$ symbol.
It's denoted with the $\cup$ symbol.
$$
\begin{aligned}
@@ -191,7 +191,7 @@ $$
The intersection of two or more sets is a set that contains all elements that belongs in all given sets.
It's denotated with the $\cap$ symbol.
It's denoted with the $\cap$ symbol.
$$
\begin{aligned}
@@ -226,7 +226,7 @@ $$
The set difference of two sets $A$ and $B$ is a set that contains all elements of $A$ that are not inside $B$.
It's denotated with the $−$ symbol and is formally defined as $A − B = \\{ x ∣ x \in A : x \notin B \\}$
It's denoted with the $−$ symbol and is formally defined as $A − B = \\{ x ∣ x \in A : x \notin B \\}$
$$
\begin{aligned}