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Intersection de
A
{\displaystyle A}
e
B
{\displaystyle B}
Union de
A
{\displaystyle A}
e
B
{\displaystyle B}
Differentia de insimules:
A
{\displaystyle A}
minus
B
{\displaystyle B}
Differentia symmetric de
A
{\displaystyle A}
e
B
{\displaystyle B}
Le theoria de insimules es un disciplina del logica occupante se de insimules como objectos del mathematica . Como le creator de iste theoria vale le mathematico german Georg Cantor (1845 - 1918).
Insimules qualcunque es indicate per majusculas
A
{\displaystyle A}
B
{\displaystyle B}
C
{\displaystyle C}
I
{\displaystyle I}
∅
{\displaystyle \emptyset }
C
{\displaystyle \mathbb {C} }
N
{\displaystyle \mathbb {N} }
Z
{\displaystyle \mathbb {Z} }
{
1
;
2
;
3
;
4
;
5
}
{\displaystyle \{1;2;3;4;5\}}
Appertinentia e inappertinentia es indicate assi:
7
∈
N
{\displaystyle 7\in \mathbb {N} }
−
7
∉
N
{\displaystyle -7\notin \mathbb {N} }
7 in N , minus 7 non in N .
Un intersection
A
∩
B
{\displaystyle A\cap B}
A
{\displaystyle A}
B
{\displaystyle B}
A
∩
B
:=
{
x
∣
x
∈
A
∧
x
∈
B
}
{\displaystyle A\cap B:=\{x\mid x\in A\wedge x\in B\}}
A intersecate con B .
Un union
A
∪
B
{\displaystyle A\cup B}
A
{\displaystyle A}
B
{\displaystyle B}
A
∪
B
:=
{
x
∣
x
∈
A
∨
x
∈
B
}
{\displaystyle A\cup B:=\{x\mid x\in A\vee x\in B\}}
A unite con B .
Le differentia
A
∖
B
{\displaystyle A\setminus B}
A
{\displaystyle A}
B
{\displaystyle B}
A
∖
B
:=
{
x
∣
x
∈
A
∧
x
∉
B
}
{\displaystyle A\setminus B:=\{x\mid x\in A\wedge x\notin B\}}
A minus B o A sin B .
Un differentia symmetric
A
△
B
{\displaystyle A\triangle B}
A
{\displaystyle A}
B
{\displaystyle B}
A
△
B
:=
(
A
∖
B
)
∩
(
B
∖
A
)
=
(
A
∩
B
)
∖
(
A
∩
B
)
{\displaystyle A\triangle B:=(A\setminus B)\cap (B\setminus A)=(A\cap B)\setminus (A\cap B)}
Si omne elemento de
A
{\displaystyle A}
B
{\displaystyle B}
A
{\displaystyle A}
subinsimul de
B
{\displaystyle B}
A
⊆
B
:⇔
∀
x
∈
A
x
∈
B
{\displaystyle A\subseteq B:\Leftrightarrow \forall x\in A\;\;x\in B}
Si
A
{\displaystyle A}
B
{\displaystyle B}
B
{\displaystyle B}
A
{\displaystyle A}
B
⊇
A
{\displaystyle B\supseteq A}
Si le insimules differe, ita
A
≠
B
{\displaystyle A\neq B}
A
{\displaystyle A}
B
{\displaystyle B}
A
⊊
B
:⇔
(
∀
x
∈
A
x
∈
B
)
∧
(
A
≠
B
)
{\displaystyle A\subsetneq B:\Leftrightarrow (\forall x\in A\;\;x\in B)\wedge (A\neq B)}
Nota que le symbolo
⊂
{\displaystyle \subset }
⊆
{\displaystyle \subseteq }
⊊
{\displaystyle \subsetneq }
