On the assumption that; supposing: Assuming the house is for sale, would you buy it?
Taking too much for granted; presumptuous. On the assumption that; supposing. Assuming the house is for sale, would you buy it? Present participle of assume. Assuming this is true, what was the price? She believes you to be interested only in assuming her position. He'd entered twice since assuming his duties. Assuming you make it that far.