With all parts included; with nothing missing; full.
After she found the rook, the chess set was complete.
Finished; ended; concluded; completed.
When your homework is complete, you can go and play with Martin.
Generic intensifier.
He is a complete bastard!
(of a metric space) In which every Cauchy sequence converges to a point within the space.
(of a lattice) In which every set with a lower bound has a greatest lower bound.
(of a category) In which all small limits exist.
(of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.
(of a problem) That is in a given complexity class and is such that every other problem in the class can be reduced to it (usually in polynomial time or logarithmic space).
One who completes something.