I am tryıng to learn locally finite and can you give an explanation for my green writing please thank you
2026-05-06 01:52:17.1778032337
Locally finite or not
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I answered the first one here: it’s not even point-finite, because $0$ is in all of the sets.
The same holds true for the cover $\{[0,n]:n\in\Bbb Z^+\}$ of $[1,\to)$: $0$ is in every one of the sets $[0,n]$, so this cover is not even point-finite. In fact, every non-negative real number is in infinitely many of these sets: if $x\ge 0$, there is an integer $n\ge x$, and then $x\in[0,k]$ for every $k\ge n$.