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inverse

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inverse


  4  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Inverse  \In*verse"\,  a.  [L.  inversus  p.  p.  of  invertere:  cf  F. 
  inverse.  See  {Invert}.] 
  1.  Opposite  in  order  relation,  or  effect;  reversed; 
  inverted;  reciprocal;  --  opposed  to  {direct}. 
 
  2.  (Bot.)  Inverted;  having  a  position  or  mode  of  attachment 
  the  reverse  of  that  which  is  usual. 
 
  3.  (Math.)  Opposite  in  nature  and  effect;  --  said  with 
  reference  to  any  two  operations,  which  when  both  are 
  performed  in  succession  upon  any  quantity,  reproduce  that 
  quantity;  as  multiplication  is  the  inverse  operation  to 
  division.  The  symbol  of  an  inverse  operation  is  the  symbol 
  of  the  direct  operation  with  -1  as  an  index.  Thus  sin-1  x 
  means  the  arc  whose  sine  is  x. 
 
  {Inverse  figures}  (Geom.),  two  figures,  such  that  each  point 
  of  either  figure  is  inverse  to  a  corresponding  point  in 
  the  order  figure. 
 
  {Inverse  points}  (Geom.),  two  points  lying  on  a  line  drawn 
  from  the  center  of  a  fixed  circle  or  sphere,  and  so 
  related  that  the  product  of  their  distances  from  the 
  center  of  the  circle  or  sphere  is  equal  to  the  square  of 
  the  radius. 
 
  {Inverse},  or  {Reciprocal},  {ratio}  (Math.),  the  ratio  of  the 
  reciprocals  of  two  quantities. 
 
  {Inverse},  or  {Reciprocal,  {proportion},  an  equality  between 
  a  direct  ratio  and  a  reciprocal  ratio;  thus  4  :  2  :  :  1/3 
  :  1/6,  or  4  :  2  :  :  3  :  6,  inversely. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Inverse  \In"verse\,  n. 
  That  which  is  inverse. 
 
  Thus  the  course  of  human  study  is  the  inverse  of  the 
  course  of  things  in  nature.  --Tatham. 
 
  From  WordNet  r  1.6  [wn]: 
 
  inverse 
  adj  1:  inversely  related;  "1/2  is  the  inverse  of  2" 
  2:  reversed  (turned  backward)  in  order  or  nature  or  effect 
  [syn:  {reverse}] 
  3:  (mathematics)  varying  in  a  manner  opposite  to  that  of 
  another  quantity;  "a  term  is  in  inverse  proportion  to 
  another  term  if  it  increases  (or  decreases)  as  the  other 
  decreases  (or  increases)  [ant:  {direct}] 
  n  1:  (math)  one  of  a  pair  of  numbers  whose  product  is  1:  the 
  reciprocal  of  2/3  is  3/2;  the  inverse  of  7  is  1/7  [syn: 
  {reciprocal}] 
  2:  something  inverted  in  sequence  or  character  or  effect;  "when 
  the  direct  approach  failed  he  tried  the  inverse"  [syn:  {opposite}] 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  inverse 
 
    Given  a  {function},  f  :  D  ->  C,  a  function  g  :  C 
  ->  D  is  called  a  left  inverse  for  f  if  for  all  d  in  D,  g  (f  d) 
  =  d  and  a  right  inverse  if  for  all  c  in  C,  f  (g  c)  =  c  and  an 
  inverse  if  both  conditions  hold  Only  an  {injection}  has  a 
  left  inverse,  only  a  {surjection}  has  a  right  inverse  and  only 
  a  {bijection}  has  inverses.  The  inverse  of  f  is  often  written 
  as  f  with  a  -1  superscript. 
 
  (1996-03-12) 
 
 




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