1 [countable] something that you consider likely to be true even though no one has told you directly or even though you have no proof
Your argument is based on a completely false assumption.
assumption that: There is an assumption that all the people who live around here are rich.
make an assumption (=make a decision based on poor evidence): People tend to make assumptions about you based on your appearance.
on the assumption that: The law works on the assumption that it is preferable for children to be with their mother.
Synonyms and related words