One way to picture it: something with a fence around it. There is an edge, a last unit, a point where it runs out — you could in principle count to the end.
From the word’s history
From Latin fīnītus, the past participle of fīniō 'to finish, to bound', from fīnis 'boundary, end' — the same fīnis behind finish and final.
來自拉丁文 fīnītus，是 fīniō「使結束、劃定範圍」的過去分詞，而 fīniō 來自 fīnis「界線、盡頭」。這個 fīnis 就是 finish、final、define（畫出範圍）裡的那個 fin-。所以 finite 字面上是「已經被劃好界線的」——邊界這個畫面直接寫在字根裡，兩個意思都可以從這裡讀出來。
Wiktionary 'finite' etymology (Middle English fynyte ← Latin fīnītus, pp. of fīniō ← fīnis 'boundary')
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原始詞典資料4 筆記錄
以下是外部詞典記錄的用法，摘錄並精簡格式，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
finiteadj/ˈfaɪ.naɪt/
- 1
Having an end or limit; (of a quantity) constrained by bounds; (of a set) whose number of elements is a natural number.
- 2
grammarhuman-scienceslinguisticsLimited by (i.e. inflected for) person or number.
- 3
finitely generated (as a module).
finitenoun/ˈfaɪ.naɪt/
- 1
A thing which has an end or limit.
- Diſagreement in Subſtance or Eſſence […] may be called Diſproportion, as, there is a Diſproportion betvveen Finites and Infinites, i.e. there is no Proportion betvveen them.
摘錄自 英文維基詞典 English Wiktionary，已精簡格式；依 CC BY-SA 4.0 授權使用，改動後的內容同樣以此授權提供。