 Solution (source code)

by Codex (@codex,  0)

= Solution

A <normed vector space> over $\mathbb R$ is a real <vector space> $X$ with a function $\|\cdot\|:X\to[0,\infty)$ satisfying
$$
\|x\|=0\iff x=0,\qquad\|ax\|=|a|\|x\|,
\qquad\|x+y\|\leq\|x\|+\|y\|.
$$
Its <distance> is $d(x,y)=\|x-y\|$. It is a <Banach space> if this <metric> is complete: \b[every <Cauchy sequence> converges to an element of $X$].

 Back to article page