${\displaystyle {}K}$

${\displaystyle {}\geq }$

${\displaystyle {}K}$

1. Aus ${\displaystyle {}a\geq b}$ folgt ${\displaystyle {}a+c\geq b+c}$ (für beliebige ${\displaystyle {}a,b,c\in K}$)
2. Aus ${\displaystyle {}a\geq 0}$ und ${\displaystyle {}b\geq 0}$ folgt ${\displaystyle {}ab\geq 0}$ (für beliebige ${\displaystyle {}a,b\in K}$)

erfüllt.

${\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }}$

${\displaystyle {}\epsilon \in \mathbb {R} }$

${\displaystyle {}\epsilon >0}$

${\displaystyle {}n_{0}\in \mathbb {N} }$

${\displaystyle {}n,m\geq n_{0}}$

${\displaystyle {}\vert {x_{n}-x_{m}}\vert \leq \epsilon \,}$

gilt.

${\displaystyle \mathbb {C} \longrightarrow \mathbb {C} ,\,z=a+b{\mathrm {i} }\longmapsto {\overline {z}}=a-b{\mathrm {i} },}$

heißt komplexe Konjugation.

${\displaystyle \varphi \colon \mathbb {R} \longrightarrow \mathbb {R} }$

${\displaystyle {}x\in \mathbb {R} }$

${\displaystyle {}\epsilon >0}$

${\displaystyle {}\delta >0}$

${\displaystyle {}\varphi {\bigl (}]x-\delta ,x+\delta [{\bigr )}\subseteq ]\varphi (x)-\epsilon ,\varphi (x)+\epsilon [\,}$

gilt.

${\displaystyle {}v_{1},\ldots ,v_{n}}$

${\displaystyle \sum _{i=1}^{n}a_{i}v_{i}=0}$

nur bei ${\displaystyle {}a_{i}=0}$ für alle ${\displaystyle {}i}$ möglich ist.

${\displaystyle \varphi \colon V\longrightarrow W}$

heißt lineare Abbildung, wenn die beiden folgenden Eigenschaften erfüllt sind.

1. ${\displaystyle {}\varphi (u+v)=\varphi (u)+\varphi (v)}$ für alle ${\displaystyle {}u,v\in V}$.
2. ${\displaystyle {}\varphi (sv)=s\varphi (v)}$ für alle ${\displaystyle {}s\in K}$ und ${\displaystyle {}v\in V}$.

${\displaystyle \sum _{k=0}^{\infty }x^{k}}$

${\displaystyle {}x}$

${\displaystyle \sum _{k=0}^{n}{\frac {f^{(k)}(a)}{k!}}(x-a)^{k}}$

heißt das Taylor-Polynom vom Grad ${\displaystyle {}n}$ zu ${\displaystyle {}f}$ im Entwicklungspunkt ${\displaystyle {}a}$.