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The statement "Nothing is impossible", a favorite phrase among self-help gurus, motivational speakers, and optimists in general, is provably false:

By contradiction:
  • Assume that nothing is impossible.
  • Create a list of impossible tasks.
  • A list of all impossible tasks will be empty.
  • A non-empty list of impossible tasks cannot exist.
  • It is impossible to create a list of impossible tasks that is not empty.
  • Something is impossible.
  • Our assumption is incorrect.

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