impossibility

[im-pos-uh-bil-i-tee, im-pos-]
noun, plural impossibilities for 2.
1.
condition or quality of being impossible.
2.
something impossible.

Origin:
1350–1400; Middle English impossibilite < Late Latin impossibilitās. See im-2, possibility

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World English Dictionary
impossibility (ɪmˌpɒsəˈbɪlɪtɪ, ˌɪmpɒs-)
 
n , pl -ties
1.  the state or quality of being impossible
2.  something that is impossible

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
The article chronicled the near impossibility of bringing a recipe to fruition
  in a conventional kitchen.
For the intelligentsia living outside, science towns held the allure of
  romantic impossibility.
We should therefore not be too disheartened by the apparent impossibility of
  building a device to perform the necessary functions.
On the impossibility of predicting the behavior of rational agents.
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