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Wiktionary
impossible dream

n. (context figuratively English) A belief or goal which is unattainable despite the pursuer's high hopes.

Wikipedia
Impossible Dream

Impossible Dream is Patty Griffin’s fifth commercially released album, and fourth studio album. It was released on April 20, 2004. The album features an unlisted song – Griffin’s mother and father singing “ The Impossible Dream” – at the end of “ Top of the World.”

Impossible Dream reached a peak of number 67 on the Billboard 200 chart, selling 16,000 copies in the United States in its first week.

Impossible Dream (advertisement)

Honda's Impossible Dream is a panoramic 2 minute long television commercial that was launched on December 2, 2005 in the United Kingdom. It anchored the "Power of Dreams" campaign which also included a website with extensive information about the series of vintage Honda vehicles that were chosen to illustrate the dreams of the founder of Honda. It features an actor ( Simon Paisley Day) singing, riding and driving across the scenic shorelines and roads of New Zealand, Twin Ring Motegi in Japan, and the Iguazu Falls in South America.

Usage examples of "impossible dream".

For an instant he wondered if escape was only an impossible dream, the wind that promised safety only a subterfuge, a trick.

Tranquility Motel, getting onto the grounds and snooping around had not seemed like an impossible dream.

Such a thing had always seemed an impossible dream, but it had suddenly become a real possibility.