                     襭 
                     -------------

6.2.5.  5 (10 )
।  襭: 6.0 (60%)

  ᫥饥 ।:
।
-----------
<ࠦ> ::= <᫮> |
                <ࠦ>+<ࠦ> |
                <ࠦ>-<ࠦ> |
                (<ࠦ>)

<᫮>   ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

   .   ணࠬ,  ஢  ࠢ쭮
 ࠦ. ᫨  ࠢ쭠,   㦭      
  "".
   ᫨  訡筠,  㦭  ""  ⥫쭮
⠭ 誮    ᨬ    -
 訡  砥 訡  ᪮.
    砫  誮 ᯮ  ।  .

   ਬ ࠡ ணࠬ:

砫쭮 ﭨ                 ᫥ ࠡ ணࠬ
Ŀ               Ŀ
1+(8)    >     1+(8)
               
砫쭮 ﭨ                 ᫥ ࠡ ணࠬ
Ŀ               Ŀ
1    >     1
               
砫쭮 ﭨ                 ᫥ ࠡ ணࠬ
Ŀ               Ŀ
1-2)    >     1-2)賰
               

襭

   । ࠦ, ਢ  ᫮ ,  ᮤ-
 ᪠箪 ᫮ -     ,
ப  㣫묨 ᪮:

<ࠦ> ::= <᫮> |                            (1)
                <᫮>+<ࠦ> |                (2)
                <᫮>-<ࠦ> |                (3)       (*)
                (<ࠦ>)                        (4)
<᫮>   ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9  (5)

      ४ᨢ । (  ) 뫠 -
⮩  筮 祢.
   ᠬ ,  

  <᫮> ::= <> | <> <᫮>
  <> ::= 0 | 1

ᮢ襭 ⭮,  ᫮ -   ᫥⥫쭮 
㫥  .
   ஬ ப  (<ࠦ>)   । (*)  
 ࠦﬨ  ⨯:

         (1+(7-(9+8)))
         7+(8)-(1-7)+6
          ⠪ .

   묨 ᫮ । (*)  ᮮ⢥ 襬 -
⨢ ।⠢  ⮬,      -
  㣫묨  ᪮.  祬 ? , ਬ, 
5-(-3) ࠦ  ᫥ ।  㤥,   ६ 
 筮   ᮢ襭 ଠ쭠  , 祭 -
ன ࠢ 8.
     ⢮   ⠪-  .
   , ਬ,   7+(6-(5))   ࠦ
 ᫥ । (*).
    (2) ᫥,   7+(6-(5))  㤥 ࠦ, ᫨
ࠦ   (6-(5)).
     (4)  ᫥,   (6-(5)) 㤥 ࠦ,  ᫨
ࠦ   6-(5).
    (3) ᫥,    6-(5) 㤥 ࠦ, ᫨ -
ࠦ   (5).
    (4) ᫥,    (5) 㤥 ࠦ, ᫨ -
   5.
       5  -  ࠦ  (1),  5 -  ᫮ 
(5).
   ࠡ   ४ᨢ묨  ।ﬨ  祭 . 
 ଠ⨪ 室  ࠭ ⥬⨪  -
.
    5+3 -  ࠦ,  5+F - .  ⭮.  ⮣-
 ( ᫮) 5+3-7 - ⮦ ࠦ.  5+3 - ࠦ 
7 - ࠦ ⮦. ⭮,   楯窠 ,  -
묨   "+"  "-" -  ࠦ.    -
  樨.
  ᬮਬ ꥪ
     Vn = <><><><> ....<>    (**)
  (᫮ n ,    (**) n  "+"  "-").
   ꥪ
     V1 = <><><> - ࠦ    ( -
樨).
    ⭮,  Vn -   ࠦ.  ⮣,
 Vn+1  ࠦ ⮦ (樮 室).
  ⥫⢮.
    祢, 
Vn+1 = Vn<><>                              (***)
    ⠪   Vn  - ࠦ ( 樮 ।),
 ꥪ (***)  ࠦ  । (*).
   祬, ,  Vn  -   ࠦ,  祢 
 类 ⥫⢠.
    㦤 ⠪.
   V1  -   ࠦ   (*).   ᫨   ࠦ  
<><>,      (*) 稬 ࠦ V2.  -
⥫쭮, ᫨  㤥 த  ⮬   (ਡ   -
ࠦ <><>),   ᥣ  㤥  ࠦ 
 n.   ᥣ Vn - 㤥 ࠦ.

 ᪮쪮 権.

ਬ ࠦ:
1) (2)
2) ((2))
3) (2+3)
4) (2+3-7)
5) (2+3)-(7+6)
6) ((2+3)-(7+6))
7) (2)-(7)
8) ((2)-(7))
9) ((2+3)-(7+6))+5

ਬ ᥩ  訡:
1)  ()
2)  (2 (+3))
3)  (2+3))
4)  )2(
5)  (2+3
6)  1+(-5)

   ,   6) ࠦ    .   뫠 
ࠦ  (*), ᫨  ࠦ 뫠  (-5).  
(-5) 뫠   ࠦ, ᫨   ࠦ 뫠  -5. 
᫥  ࠦ  ,     -
 (*)  ࠧ  "-5"  室.
   ᫥ ਬ 室  訬 ।⠢  ࠢ-
 ࠦ   ᪮.  ந室 ⮬,  ᫮ 
  筮    ᫮  ᫥ ।-
 (*).  । (*) ᫮  -      ᮤ-
.

    襭    ᭮   ࠬ 室 
 ﭨ    㣨  ⥫  
㣫 ᪮ ( 奬   ࠦ):

                                        (訡)
                                           ^
                                  ⠫쭮
                                            Ŀ
                                              )
                       Ŀ    
                                        V    V  
                                        (᪮))  (⢥)
                       )                  +,-
                                          
                                          
                                V      ⠫쭮
 (⢥) < (᫮) < (  室  ) > (訡)
                                      ^    ^
                         +,-              
            ⠫쭮                     
(訡) <       
                                          (  
                                             
                                          

    ᫥    ᮬ 㣫 ᪮ 㤥 ᯮ짮
騪 ४  (砫쭮  ⮩).    뢠饩
᪮ 㤥 ਬ  騪  ,     -
뢠饩 - .  ᫨  ᫥ ᬮ ᥣ ࠦ 騪
 㤥 ,  訡.  ᪮   襭.
   ⠪, ࠬ ﭨ 㤥 "᫥"   ࠢ筮
 㣫 ᪮    ,  騪 -  -
ᮬ ᪮.
   ᫨, ਬ,  ᫮  ᯮ  뢠 ᪮
(訡!),  ࠬ ﭨ  砩 ।ᬠਢ.
     ᯮ 訡   "2+3)" ࠬ ᨫ쭠!
 뢠 ᪮  ᫮ -    ଠ-
.   訡  ன ᫥  ᮤন 騪.


 室0                             騪 㤥 ᯮ짮  
                                  㣫 ᪮  ࠦ.
                             砫 ⨬  騪 
                                  ३  ﭨ (室).
 室                                
                                
                                     
 室                             
                               誮  ᫥騩 ᨬ .
          ᫮             ᫮.
   (  室1               楤 "室1" 믮  騪
  訡                           ୥  
                                ﭨ (室) ᮣ᭮ ࠬ.
                                     
 室1                            ⨫ ᪮ "(".
                                ਬ  騪  .
                                 
                                
  室                               
                                
                                     
 ᪮)                          ⨫ ᪮ ")".
                               誮  ᫥騩 ᨬ .
                                ਬ  騪  ,
                                     ᫨   ஢ਬ ४⭮
    {   訡 }᫥饣 ᨬ.
                                
 {                                   
                                
                                
           +  室             
      -  室             
       ⢥         
     )  ᪮)           
    訡                      
 }                                   
                                
                                     
 ᫮                              ᫮.
                               誮  ᫥騩 ᨬ .
    ⢥                 
   +  室                
   -  室                
   )  ᪮)             
  訡                        
                                
                                     
 ⢥                            
                               
                                
                        ०, 祬    "",
 {                                   ஢ਬ  襭   
     訡                 ᪮.
 }                                   
                                
 {                                   
                          
                      
 }                                   
                                
                                     
 訡                           
                               
                            
   ⢥_訡                    
   訡                       
                                
                                
                                     
 ⢥_訡                     
                          
                          
  2                      
                                


  訡  襭.

   1) ணࠬ ࠡ  室 ⬠.

   2) ୮ 㪠뢠  訡  .
   ਬ
   )  ஢થ ᥩ ⨯ "(2+3"   ⢥  訡
㪠뢠 뢠 ᪮.   ⨪  訡 
 ४⭮.  ᪮     ୮ .
, 室  ,      ६  
᪮.  ⮫쪮  ⮣,      ,    
᢮  ࠧ஢      ᨬ ⠭  ,
  訡.

   )   ⨯ ")(", "()", "1(+2)", "1()"  ⢥ -
筮 ᨬ  㪠뢠  ࢠ ⪠  ᫥ .
  ୮.  ⢥   ᫥饩 ப:
")(", "()", "1(+2)", "1()"
 ^      ^     ^        ^
   ) ୮ 㪠  訡  : (1+1
                                                ^
