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impossibility (n.)

late 14c., "quality of being impossible," from impossible + -ity; perhaps from or modeled on Old French impossibilité (14c.). Meaning "an impossible thing or occurrence" is from c. 1500. Sometimes in English 15c.-18c. it meant "inabolity, impotence," after a use of Medieval Latin impossibilitas.

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Definitions of impossibility from WordNet

impossibility (n.)
incapability of existing or occurring;
Synonyms: impossibleness
impossibility (n.)
an alternative that is not available;
Synonyms: impossible action
From wordnet.princeton.edu