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Meanings of finitely in English

With a finite limit.

Usage of finitely in English
1
Jack sighed, looking at the floor between them, shaking finitely all over his body.
Street magic
2
For degree 5 and higher, a theorem of Gerd Faltings (a 1986 Fields Medalist) says that there are only finitely many rational points.
The Guardian
Finitely through the time