An assumption.
"The project was delayed based on an assumption that funding would be approved by next week."
present participle of assume
"Assuming you have finished your work, we can leave early today."
In plain English: Assuming means taking something to be true without having proof that it is actually correct.
"He kept pushing the conversation forward, assuming we were still going to dinner together."
excessively forward
"an assumptive person"
"on a subject like this it would be too assuming for me to decide"
"the duchess would not put up with presumptuous servants"
haughty; arrogant
"The new manager spoke to everyone in an assuming tone, as if her opinions were the only ones that mattered."