MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

1 like 0 dislike
47 views
Let $(u, v, w) \in(0,1) \times(0,1) \times(0,1)$ [the "unit open cube" in $\left.\mathbb{R}^{3}\right]$. What is an $\varepsilon>0$ such that $B((u, v, w) ; \varepsilon) \subset(0,1) \times(0,1) \times(0,1) ?$
| 47 views

1 like 0 dislike
Let $\varepsilon=\min \{u, 1-u, v, 1-v, w, 1-w\} .$ Since $(u, v, w) \in(0,1) \times(0,1) \times(0,1)$. Then $0<u<1,0<v<1$,
and $0<w<1$. Thus, $u, 1-u, v, 1-v, w$, and $1-w$ are all positive. Since the minimum of positive numbers is positive, $\varepsilon>0$.
by Bronze Status (8,688 points)

0 like 0 dislike