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be under no illusion
To know and understand the reality or truth of a situation. Don't worry, I'm not getting back together with Alex. After all his lies, I'm under no illusion about how he operates.
be under the illusion that
To be living, operating, or functioning based on a belief that is fanciful, unrealistic, or untrue. Jeremy's always been under the illusion that he's a great writer, even though he's never written more than a few crummy poems. No one likes paying taxes, but those who would call for them to be done away with altogether are under the illusion that our society can function without them.
labor under the illusion of/that
To live, operate, or function with the unyielding belief in something, especially that which is fanciful, unrealistic, or untrue. Primarily heard in US. Jeremy's always labored under the illusion of being a great writer, even though he's never written more than a few crummy poems. No one likes paying taxes, but those who would call for them to be done away with altogether are laboring under the illusion that our society can function without them!
be under the illusion thatwrongly believe that.
1998 Independent The keening harmonies of the Brothers Gibb, a million naff dance routines by medallion men under the illusion that they were John Travolta.
be under no illusion (or illusions)be fully aware of the true state of affairs.
1992 Christian Scientist Monitor It is crucial to the nation's security…that we be under no illusions about reasons for this zero-loss rate.