I had a question, Does "take someone up on something " mean only to accept an offer ? Can it mean to accept a suggestion
In most of the dictionaries like Cambridge and Macmillan had this definition:to accept an offer. But in Idoceonline ,it had a few sentences which I couldn't guess the meaning of: https://www.ldoceonline.com/dictionary/take-up-on
•You don't take me up on anything - you just repeat it in a different order.
• At least six thousand Mennonites took her up on it.
• I offered myself up to be corrupted, but nobody took me up on it.
• Might take her up on it.
• What if I should take you up on it?
P.S. An offer can be something like: She offered me a movie ticket. (Or any other offer,maybe do something) and suggestion is sort of an advice or something like: you could do it this way (or something like telling someone to do something).
What is it actually used for in America? And what exactly do those sentences mean?