1. Should old acquaintance be forgot,

and old lang syne?

2. Should old acquaintance be forgot,
and should old lang syne be forgot?
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Does #1 mean #2?

auld lang sine or old lang sine means "the old days" according to Cambridge dictionary. [ Auld lang syne means "the old days" in Scots.]

[Auld Lang Syne means ‘for old time’s sake’. - Macmillan Dictionary]

Is 'the old day' the same as ‘for old time’s sake’?

https://www.rd.com/culture/what-does-auld-lang-syne-mean/

Read carefully.

1. Both #1 and #2 are variations of the same phrase from the song "Auld Lang Syne" by Robert Burns. However, #1 is a more commonly used version. Both versions convey the idea of remembering and cherishing old times and old friends.

2. In the context of the lyrics of the song, "Should old acquaintance be forgot, and should old lang syne be forgot?" is a rhetorical question. It emphasizes the desire to remember and not forget the old days and old friends.

Now, onto the meaning of "auld lang syne" or "old lang syne":

- According to the Cambridge Dictionary, "auld lang syne" means "the old days" in Scots, which refers to memories and experiences from the past.

- The Macmillan Dictionary suggests that "auld lang syne" means "for old time’s sake." This phrase implies doing something or having a sentimental attachment to something out of nostalgia or as a tribute to past experiences and relationships.

To answer your question, "the old day" and "for old time’s sake" convey a similar idea, emphasizing nostalgia and memories of the past. They are different expressions to capture the sentiment behind "auld lang syne."