Odległość punktów
(
2
2
,
2
2
)
{\displaystyle {\bigg (}{\frac {\sqrt {2}}{2}},{\frac {\sqrt {2}}{2}}{\bigg )}}
(
−
2
2
,
−
2
2
)
{\displaystyle {\bigg (}-{\frac {\sqrt {2}}{2}},-{\frac {\sqrt {2}}{2}}{\bigg )}}
R
2
{\displaystyle \mathbb {R} ^{2}}
d
1
{\displaystyle d_{1}}
d
2
{\displaystyle d_{2}}
Dobrze
d
2
{\displaystyle d_{2}}
d
∞
{\displaystyle d_{\infty }}
Dobrze
d
∞
{\displaystyle d_{\infty }}
d
1
{\displaystyle d_{1}}
Źle
{
a
n
}
⊆
(
R
2
,
d
2
)
{\displaystyle \{a_{n}\}\subseteq (\mathbb {R} ^{2},d_{2})}
a
n
=
(
(
−
1
)
n
1
n
,
(
−
1
)
n
)
{\displaystyle a_{n}={\bigg (}(-1)^{n}{\frac {1}{n}},(-1)^{n}{\bigg )}}
Źle
R
2
{\displaystyle \mathbb {R} ^{2}}
Źle
Dobrze
A
{\displaystyle A}
(
1
,
1
)
{\displaystyle (1,1)}
1
{\displaystyle 1}
R
2
{\displaystyle \mathbb {R} ^{2}}
d
1
{\displaystyle d_{1}}
(
0
,
0
)
{\displaystyle (0,0)}
2
{\displaystyle 2}
d
1
{\displaystyle d_{1}}
Źle
(
0
,
0
)
{\displaystyle (0,0)}
2
{\displaystyle 2}
d
2
{\displaystyle d_{2}}
Źle
(
0
,
0
)
{\displaystyle (0,0)}
2
{\displaystyle 2}
d
∞
{\displaystyle d_{\infty }}
Dobrze
1
4
,
1
9
,
1
16
,
1
25
,
1
36
,
…
{\displaystyle {\frac {1}{4}},{\frac {1}{9}},{\frac {1}{16}},{\frac {1}{25}},{\frac {1}{36}},\ldots }
{
1
n
}
n
∈
N
{\displaystyle {\bigg \{}{\frac {1}{n}}{\bigg \}}_{n\in \mathbb {N} }}
Dobrze
{
1
n
2
}
n
∈
N
{\displaystyle {\bigg \{}{\frac {1}{n^{2}}}{\bigg \}}_{n\in \mathbb {N} }}
Dobrze
{
1
2
n
}
n
∈
N
{\displaystyle {\bigg \{}{\frac {1}{2n}}{\bigg \}}_{n\in \mathbb {N} }}
Źle
⋂
n
=
1
∞
[
−
1
n
,
1
n
]
{\displaystyle \bigcap _{n=1}^{\infty }{\bigg [}-{\frac {1}{n}},{\frac {1}{n}}{\bigg ]}}
{
0
}
{\displaystyle \{0\}}
Dobrze
∅
{\displaystyle \emptyset }
Źle
⋂
n
=
1
∞
(
−
1
n
,
1
n
)
{\displaystyle \bigcap _{n=1}^{\infty }{\bigg (}-{\frac {1}{n}},{\frac {1}{n}}{\bigg )}}
Dobrze
{
a
n
}
{\displaystyle \{a_{n}\}}
(
R
4
,
d
2
)
{\displaystyle (\mathbb {R} ^{4},d_{2})}
a
n
=
(
(
−
1
)
n
,
1
n
,
(
−
1
)
n
1
n
,
(
−
1
)
n
+
1
)
{\displaystyle a_{n}={\bigg (}(-1)^{n},{\frac {1}{n}},(-1)^{n}{\frac {1}{n}},(-1)^{n+1}{\bigg )}}
a
n
{\displaystyle a_{n}}
(
1
,
0
,
0
,
1
)
{\displaystyle (1,0,0,1)}
Źle
a
n
{\displaystyle a_{n}}
(
−
1
,
0
,
0
,
1
)
{\displaystyle (-1,0,0,1)}
Dobrze
Parser nie mógł rozpoznać (SVG (MathML może zostać włączone przez wtyczkę w przeglądarce): Nieprawidłowa odpowiedź („Math extension cannot connect to Restbase.”) z serwera „https://wazniak.mimuw.edu.pl/api/rest_v1/”:): {\displaystyle a_n}
jest rozbieżny Dobrze
![{\displaystyle \bigcap _{n=1}^{\infty }{\bigg [}-{\frac {1}{n}},{\frac {1}{n}}{\bigg ]}}](https://wazniak.mimuw.edu.pl/api/rest_v1/media/math/render/svg/6854437ac0914b95a359a4e10f84451a98555c6d)
