Webster's English Dictionary

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complement

1. com.ple.ment \'ka:m-pl*-m*nt\ n [ME, fr. L complementum, fr. comple-re] 
   1a: something that fills up, completes, or makes perfect  1b: the quantity 
   or number required to make a thing complete; specif  : the whole force or 
   personnel of a ship 1c: one of two mutally completing parts : COUNTERPART  
   2: the amount of angle or arc by which a given angle or arc falls short of  
   90 degrees 3: the interval in music required with a given interval to 
   complete the oct ave 4: an added word or expression by which a predication 
   is made complete (as  president in "they elected him president") 5: the 
   thermolabile substance in normal blood serum and plasma that in comb 
   ination with antibodies causes the destruction of bacteria, foreign blood 
   corpuscles, and other antigens
2. com.ple.ment \-.ment\ vt 1: to be complementary to  obs  2: COMPLIMENT  
   obs  : to exchange formal courtesies