a false or wrong belief or ideaillusion that: Many people still have the illusion that full employment is possible.
create/give/maintain the illusion: This description creates the illusion that we can solve all our environmental problems.
be under no illusion/illusions (=not have a false idea): We are under no illusion that this money will be enough.
have no illusions (=realize that something is difficult or unpleasant): I had no illusions about the task that lay ahead.