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inverse

## 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

{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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