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function

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function


  6  definitions  found 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Function  \Func"tion\,  n. 
  1.  (Eccl.)  A  religious  ceremony,  esp.  one  particularly 
  impressive  and  elaborate. 
 
  Every  solemn  `function'  performed  with  the 
  requirements  of  the  liturgy.  --Card. 
  Wiseman. 
 
  2.  A  public  or  social  ceremony  or  gathering;  a  festivity  or 
  entertainment,  esp.  one  somewhat  formal. 
 
  This  function,  which  is  our  chief  social  event.  --W. 
  D.  Howells. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Fluent  \Flu"ent\,  n. 
  1.  A  current  of  water;  a  stream.  [Obs.] 
 
  2.  [Cf.  F.  fluente.]  (Math.)  A  variable  quantity,  considered 
  as  increasing  or  diminishing;  --  called  in  the  modern 
  calculus,  the  {function}  or  {integral}. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Function  \Func"tion\,  n.  [L.  functio,  fr  fungi  to  perform, 
  execute,  akin  to  Skr.  bhuj  to  enjoy,  have  the  use  of:  cf  F. 
  fonction.  Cf  {Defunct}.] 
  1.  The  act  of  executing  or  performing  any  duty,  office,  or 
  calling;  per  formance.  ``In  the  function  of  his  public 
  calling.''  --Swift. 
 
  2.  (Physiol.)  The  appropriate  action  of  any  special  organ  or 
  part  of  an  animal  or  vegetable  organism;  as  the  function 
  of  the  heart  or  the  limbs;  the  function  of  leaves,  sap, 
  roots,  etc.;  life  is  the  sum  of  the  functions  of  the 
  various  organs  and  parts  of  the  body. 
 
  3.  The  natural  or  assigned  action  of  any  power  or  faculty,  as 
  of  the  soul,  or  of  the  intellect;  the  exertion  of  an 
  energy  of  some  determinate  kind 
 
  As  the  mind  opens,  and  its  functions  spread.  --Pope. 
 
  4.  The  course  of  action  which  peculiarly  pertains  to  any 
  public  officer  in  church  or  state;  the  activity 
  appropriate  to  any  business  or  profession. 
 
  Tradesmen  .  .  .  going  about  their  functions.  --Shak. 
 
  The  malady  which  made  him  incapable  of  performing 
  his  regal  functions.  --Macaulay. 
 
  5.  (Math.)  A  quantity  so  connected  with  another  quantity, 
  that  if  any  alteration  be  made  in  the  latter  there  will  be 
  a  consequent  alteration  in  the  former.  Each  quantity  is 
  said  to  be  a  function  of  the  other  Thus  the 
  circumference  of  a  circle  is  a  function  of  the  diameter. 
  If  x  be  a  symbol  to  which  different  numerical  values  can 
  be  assigned,  such  expressions  as  x^{2},  3^{x},  Log  x,  and 
  Sin.  x,  are  all  functions  of  x. 
 
  {Algebraic  function},  a  quantity  whose  connection  with  the 
  variable  is  expressed  by  an  equation  that  involves  only 
  the  algebraic  operations  of  addition,  subtraction, 
  multiplication,  division,  raising  to  a  given  power,  and 
  extracting  a  given  root;  --  opposed  to  transcendental 
  function. 
 
  {Arbitrary  function}.  See  under  {Arbitrary}. 
 
  {Calculus  of  functions}.  See  under  {Calculus}. 
 
  {Carnot's  function}  (Thermo-dynamics),  a  relation  between  the 
  amount  of  heat  given  off  by  a  source  of  heat,  and  the  work 
  which  can  be  done  by  it  It  is  approximately  equal  to  the 
  mechanical  equivalent  of  the  thermal  unit  divided  by  the 
  number  expressing  the  temperature  in  degrees  of  the  air 
  thermometer,  reckoned  from  its  zero  of  expansion. 
 
  {Circular  functions}.  See  {Inverse  trigonometrical  functions} 
  (below).  --  Continuous  function,  a  quantity  that  has  no 
  interruption  in  the  continuity  of  its  real  values,  as  the 
  variable  changes  between  any  specified  limits. 
 
  {Discontinuous  function}.  See  under  {Discontinuous}. 
 
  {Elliptic  functions},  a  large  and  important  class  of 
  functions,  so  called  because  one  of  the  forms  expresses 
  the  relation  of  the  arc  of  an  ellipse  to  the  straight 
  lines  connected  therewith. 
 
  {Explicit  function},  a  quantity  directly  expressed  in  terms 
  of  the  independently  varying  quantity;  thus  in  the 
  equations  y  =  6x^{2},  y  =  10  -x^{3},  the  quantity  y  is  an 
  explicit  function  of  x. 
 
  {Implicit  function},  a  quantity  whose  relation  to  the 
  variable  is  expressed  indirectly  by  an  equation;  thus  y 
  in  the  equation  x^{2}  +  y^{2}  =  100  is  an  implicit 
  function  of  x. 
 
  {Inverse  trigonometrical  functions},  or  {Circular  function}, 
  the  lengths  of  arcs  relative  to  the  sines,  tangents,  etc 
  Thus  AB  is  the  arc  whose  sine  is  BD  and  (if  the  length 
  of  BD  is  x)  is  written  sin  ^{-1}x,  and  so  of  the  other 
  lines.  See  {Trigonometrical  function}  (below).  Other 
  transcendental  functions  are  the  exponential  functions, 
  the  elliptic  functions,  the  gamma  functions,  the  theta 
  functions,  etc 
 
  {One-valued  function},  a  quantity  that  has  one  and  only  one 
  value  for  each  value  of  the  variable.  --  {Transcendental 
  functions},  a  quantity  whose  connection  with  the  variable 
  cannot  be  expressed  by  algebraic  operations;  thus  y  in 
  the  equation  y  =  10^{x}  is  a  transcendental  function  of  x. 
  See  {Algebraic  function}  (above).  --  {Trigonometrical 
  function},  a  quantity  whose  relation  to  the  variable  is  the 
  same  as  that  of  a  certain  straight  line  drawn  in  a  circle 
  whose  radius  is  unity,  to  the  length  of  a  corresponding 
  are  of  the  circle.  Let  AB  be  an  arc  in  a  circle,  whose 
  radius  OA  is  unity  let  AC  be  a  quadrant,  and  let  OC  DB 
  and  AF  be  drawnpependicular  to  OA  and  EB  and  CG  parallel 
  to  OA  and  let  OB  be  produced  to  G  and  F.  E  Then  BD  is  the 
  sine  of  the  arc  AB  OD  or  EB  is  the  cosine,  AF  is  the 
  tangent,  CG  is  the  cotangent,  OF  is  the  secant  OG  is  the 
  cosecant,  AD  is  the  versed  sine,  and  CE  is  the  coversed 
  sine  of  the  are  AB  If  the  length  of  AB  be  represented  by 
  x  (OA  being  unity)  then  the  lengths  of  Functions.  these 
  lines  (OA  being  unity)  are  the  trigonometrical  functions 
  of  x,  and  are  written  sin  x,  cos  x,  tan  x  (or  tang  x),  cot 
  x,  sec  x,  cosec  x,  versin  x,  coversin  x.  These  quantities 
  are  also  considered  as  functions  of  the  angle  BOA. 
 
  From  Webster's  Revised  Unabridged  Dictionary  (1913)  [web1913]: 
 
  Function  \Func"tion\,  Functionate  \Func"tion*ate\,  v.  i. 
  To  execute  or  perform  a  function;  to  transact  one's  regular 
  or  appointed  business. 
 
  From  WordNet  r  1.6  [wn]: 
 
  function 
  n  1:  a  mathematical  relation  such  that  each  element  of  one  set  is 
  associated  with  at  least  one  element  of  another  set 
  [syn:  {mathematical  function}] 
  2:  what  something  is  used  for  "the  function  of  an  auger  is  to 
  bore  holes";  "ballet  is  beautiful  but  what  use  is  it?" 
  [syn:  {purpose},  {role},  {use}] 
  3:  the  actions  and  activities  assigned  to  or  required  or 
  expected  of  a  person  or  group:  "the  function  of  a 
  teacher";  "the  government  must  do  its  part"  or  "play  its 
  role"  or  "do  its  duty"  [syn:  {office},  {part},  {role}] 
  4:  a  relation  such  that  one  thing  is  dependent  on  another; 
  "height  is  a  function  of  age";  "price  is  a  function  of 
  supply  and  demand" 
  5:  a  formal  or  official  social  gathering  or  ceremony;  "it  was  a 
  black-tie  function" 
  6:  a  set  sequence  of  steps,  part  of  larger  computer  program 
  [syn:  {routine},  {subroutine},  {subprogram},  {procedure}] 
  v  1:  function  properly;  "The  washing  machine  won't  go  unless  it's 
  plugged  in"  [syn:  {work},  {operate},  {go},  {run}]  [ant: 
  {malfunction}] 
  2:  serve  a  purpose,  role,  or  function;  "The  tree  stump  serves 
  as  a  table";  "The  female  students  served  as  a  control 
  group";  "This  table  would  serve  very  well";  "His  freedom 
  served  him  well";  The  table  functions  as  a  desk"  [syn:  {serve}] 
  3:  act  as  an  official  in  a  specific  function  [syn:  {officiate}] 
 
  From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]: 
 
  function 
 
  1.    (Or  "map",  "mapping")  If  D  and  C  are  sets 
  (the  domain  and  codomain)  then  a  function  f  from  D  to  C, 
  normally  written  "f  :  D  ->  C"  is  a  subset  of  D  x  C  such  that: 
 
  1.  For  each  d  in  D  there  exists  some  c  in  C  such  that  (d,c)  is 
  an  element  of  f.  I.e.  the  function  is  defined  for  every 
  element  of  D. 
 
  2.  For  each  d  in  D,  c1  and  c2  in  C,  if  both  (d,c1)  and  (d,c2) 
  are  elements  of  f  then  c1  =  c2.  I.e.  the  function  is  uniquely 
  defined  for  every  element  of  D. 
 
  See  also  {image},  {inverse},  {partial  function}. 
 
  2.    Computing  usage  derives  from  the  mathematical 
  term  but  is  much  less  strict.  In  programming  (except  in 
  {functional  programming}),  a  function  may  return  different 
  values  each  time  it  is  called  with  the  same  argument  values 
  and  may  have  {side  effects}. 
 
  A  {procedure}  is  a  function  which  returns  no  value  but  has 
  only  {side-effects}.  The  {C}  language,  for  example,  has  no 
  procedures,  only  functions.  {ANSI  C}  even  defines  a  {type}, 
  {void},  for  the  result  of  a  function  that  has  no  result. 
 
  (1996-09-01) 
 
 




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