Giuseppe Bilotta

#math #lexicon question (sorry, I studied these things in Italian, so I don't know the English term). How do you call a sequence or series whose terms have alternating signs *but only after a few terms*?

Think something like
1 1 1 1 1 1 1 1 -1 1 -1 1 -1 ...

#mathHelp

Jun 21, 2025 at 9:32pmWeb
Show threadIzzyJun 21, 2025

@giuseppebilotta I'm not aware of this having a pre-defined name, but in English we use the word "eventually" to describe a property of a sequence or series etc. that doesn't hold at first but then does for every term after some point. For example, in a finite metric space, the only Cauchy sequences are the eventually constant ones, and this means that every finite metric space is complete.

In that vein, I would call this an "eventually alternating sequence/series", and I would expect the meaning to be intuitive to another English speaker.

Out of curiosity, what's the Italian word for this that you have in mind?

Show threadGiuseppe BilottaJun 21, 2025

@ijk oh thank you very much, that's exactly the term I was looking for. And I'm pretty sure I've come across the term before in English scientific literature, but for some reason I couldn't dig it up from memory.

FWIW, In Italian the word with the same meaning is “definitivamente” (which would literally translate as “definitely”). An “eventually alternating sequence” would be a “successione definitivamente a segno alterno”.