dense

C1 · Advanced Academic

adj. containing a lot of information or difficult ideas that make it hard to read or follow.

adj. intellectually challenging due to a high concentration of complex ideas or obscure language.

“I found the first chapter of the philosophy book very dense and had to read it twice.”

“The report was so dense with technical jargon and statistical data that even the experts struggled to extract a clear policy recommendation.”

C2 · Proficiency Mathematics Technical

adj. used in math to describe a set where you can always find a point between any two other points.

adj. describing a subset of a topological space whose closure is the space itself; every point in the space is a limit point of the set.

“The teacher explained that rational numbers are dense because there is always another fraction between any two.”

“In any interval of the real line, the set of rational numbers is dense, ensuring that any real number can be approximated by a sequence of rationals.”

B2 · Upper Intermediate Informal

adj. a slightly rude way to describe someone who does not understand things quickly.

adj. exhibiting a lack of mental agility or failing to grasp obvious points; slow-witted.

“I felt a bit dense when I realized the answer was right in front of me the whole time.”

“He was usually quite sharp, but he seemed uncharacteristically dense when we tried to explain the new office procedures to him.”