Ordnet man den natürlichen Zahlen (
N
=
{
1
,
2
,
3
,
…
}
{\displaystyle \mathbb {N} =\lbrace 1,2,3,\ldots \rbrace }
a
1
,
a
2
,
a
3
,
…
{\displaystyle a_{1},a_{2},a_{3},\ldots }
n
↦
a
n
{\displaystyle n\mapsto a_{n}}
1
2
3
4
5
... (natürliche Zahlen)
↓
{\displaystyle \downarrow }
↓
{\displaystyle \downarrow }
↓
{\displaystyle \downarrow }
↓
{\displaystyle \downarrow }
↓
{\displaystyle \downarrow }
a
1
{\displaystyle a_{1}}
a
2
{\displaystyle a_{2}}
a
3
{\displaystyle a_{3}}
a
4
{\displaystyle a_{4}}
a
5
{\displaystyle a_{5}}
... (reelle Zahlen)
Sei
I
{\displaystyle {\mathcal {I}}}
N
{\displaystyle \mathbb {N} }
X
{\displaystyle {\mathcal {X}}}
a
:
I
→
X
{\displaystyle a:{\mathcal {I}}\rightarrow {\mathcal {X}}}
Die Elemente
a
1
,
a
2
,
a
3
,
…
{\displaystyle a_{1},a_{2},a_{3},\ldots }
Das Element
a
0
{\displaystyle a_{0}}
a
1
{\displaystyle a_{1}}
Meistens werden Folgen in der Form
(
a
)
n
{\displaystyle (\mathbf {a} )_{\mathbf {n} }}
(
a
n
)
n
{\displaystyle (\mathbf {a} _{\mathbf {n} })_{\mathbf {n} }}
Manchmal werden auch nur die ersten Folgenglieder angegeben Mit
(
1
n
)
n
∈
N
{\displaystyle \left({\frac {1}{n}}\right)_{n\in \mathbb {N} }}
1
,
1
2
,
1
3
,
1
4
,
…
{\displaystyle 1,{\frac {1}{2}},{\frac {1}{3}},{\frac {1}{4}},\ldots }
f
:
N
→
R
,
n
↦
1
n
{\displaystyle f:\mathbb {N} \rightarrow \mathbb {R} ,n\mapsto {\frac {1}{n}}}
Durch
a
0
:=
1
{\displaystyle a_{0}:=1}
a
1
:=
1
{\displaystyle a_{1}:=1}
a
n
+
2
:=
a
n
+
1
+
a
n
{\displaystyle a_{n+2}:=a_{n+1}+a_{n}}
1
,
1
,
2
,
3
,
5
,
8
,
13
,
…
{\displaystyle 1,1,2,3,5,8,13,\ldots }
Fibonacci-Zahlen definiert. (Rekursive Definition) 
