Learner's definition of ASSUMPTION
1 [count] : something that is believed to be true or probably true but that is not known to be true : something that is assumed
I made the assumption that he was coming, so I was surprised when he didn't show up.
He will come home tomorrow. At least, that's my assumption.
Many scientific assumptions about Mars were wrong.
We are operating on/under/with the assumption that the loan will be approved. [=we are assuming that the loan will be approved; we are behaving as though we know that the loan will be approved]
I'm telling you our arrival time on the assumption that you will check to see whether or not our flight is on time before you come to the airport.
Her plan is based on the underlying assumption that the economy will improve in the near future.
2 [noncount] : the act of assuming something: such as a : the act of beginning a role, duty, etc. b : the act of taking or beginning to have power, control, etc., in a job or situation c : the act of accepting a responsibility, debt, etc.