noun (n)

• the quality of being one of a kind(noun.attribute)

  Example:
  That singularity distinguished him from all his companions.
  

  Synonym:
  uniqueness
  

  source: wordnet30
• strangeness by virtue of being remarkable or unusual(noun.attribute)

  source: wordnet30
• The quality or state of being singular; some character or quality of a thing by which it is distinguished from all, or from most, others; peculiarity.(noun)

  source: webster1913