Матан Лекции
.PDFcom.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 2. ( / #
* %#/ 0 #' * ( + #*" (# + $ 0 ) 7 # 0 ( ) #) * & " # 1 0
#) * + *. +#, 0 ) * * # + 7 ## !" 0 ( #' * + ! * # " (#
+ #* |
+ # # # . 8 0 3 + # #+ , 2 " (# + +#( * 3 * ( + #/, * !" |
+ +, |
+ ) 6#" ( #/ $ ( !" / #' # ( 0 * + , 2 + 0 2 # #* !' |
# # !' * * 3 % # + / # ) * + 0 #'. |
2.
6 * + & #) * + ) 3 # + # 0 3 0 !" * 3#' #) * #0. + 2(, ) 3 7# * + !" ) !", * %# #* + + 3 * # !+ ' # #, * # * ( * # *+ ' ! #** ( + #/ # ( + #/ + #& " ( / * ( + # ( 2 7 # +. 4 &, ! #) * #0
+ + ( 6#" #+ *# " **## # # #* # ) 3 # #, * # / *+ # +0& /(! * # %# |
& % **. |
|||
%, #0+ * #) * + |
#&, #* |
!" + " ) * #" +. |
|
|
* * + |
, +* * 3#/ 0 #) ! |
0 ) # |
# ) * + #* #/. ( 2 )7 #0 #0( |
& ( |
+ % |
. .2( +* & 0 #, ) "# * 0 +#*# +!3 & +#) & 3 / #' # #" 0+# #/ |
* & * 2 . .1 +!" " + /( # * ( 0 + */ 0 3 0 ! # * # #& #. 0 #03 ( # # * ( ( !" * 3#', #* + ( 6#" *" ( ! % %##, # 3 #0 # #0 2 #
#+ *#.
* #* ( !" ) 3 # + (+ / + #, 7# #0+ * ! # ) ! #, ( + +7# #
#) * #' #0 + * +* #+ *# # * +* $#0#-" #) * # * #.
1. . .# * #', * #) * & #0, .1-2, .: , 1975. 2. ,. .( /+% +, #) * #' #0, .1-2,.:!*7 / , 1973.
# * #* 3 * * 7 !" , * )#+ 6# 2 3* + #/ #, -2
* ( 2 6 #* 6# !' 0 * 0 ( ), # +, 0 !7 #', # * # 6#" #) * # 2 #/.
3. . .#" & %, * (#$$ %# & # # & & #*)#* #/, .1-3, .: , 1969.
#7 ( 2# (+ " # # +, + 0 ! # (! + 0& + /+7#" $( #) * & #0
+* & #+ *#.
10
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 3. 0( ! 1 ' # # + * #) * & #0
4. . ./ +, . .4 3 +, . .." +, * #) * & #0, .1-2, +: 0( * + +* &
#+ *#, 1981.
0 0 3 2 !" + + +!( # 0 ) !" # + . # ,.+ %, #* +7#" * + ! ) 3 # # +!* & + / ! * & * #.
5. . , #$$ %# #*)#* #. #$$ %# ! $!, .:#, 1971. 6. ,.+ %, #0, .1-2, .:#, 1972.
#)# ) 3 # +, * #* 0 ( ) # + #) * #0 *# * ( , 0 * ( 2# * 6#' **#) * #' *3 # 4...#( +#).
7. 4...#( +#), 3 # 0 ( ) # 2 #' #) * #0, ,: , 1966.
( ) ! )# */ 0 ( ) # # + * +* & #+ *#.
8. . .# & ( +, . ." #, . .( + #)#', -( )# # 2 #/ #) * #0, .:0( * + * +* & #+ *#, 1988.
3. |
|
|
) #) * & #0 +" (/ + & * 7#" ** + * ( ' 7 !. ( #/ ( +, |
' |
|
* + #*)#* # 3 * ) !", * #7 * 2 , ) 3! 3! * & #0 2 |
' 1 /0!. . 1 ' |
|
#)# #+ *# * #' * + / 0 + # * ( + * ', |
( # !+ * |
$ %##, |
(#$$ %# #*)#* #, / # + 3 0 ' # *+ '* +, # & #*)#* #.
* +!*7 ' # # # */ ) * *+ ( #', */6#"*/ # #) * 3 * ( & 3 0 + #/. !( # * ( 6# !.
1. .# %# ' #) * ' # ( %##.
0 ) */ + + * + ( #+ * # & *+ '* + A = A(n) ( / +* " !" )#* n. .# # '
#) * ' # ( %## * * # + + * + ( #+ * # *+ '* + A(1) ( / (# #%!, +!* 0!+ ## 0! * + ( #+ * # *+ '* + A(n) # + *+ '* + A(n + 1) ( / )#* n + 1.
11
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 3. 0( ! 1 ' # # + * #) * & #0
2. +* " ) + 3 * ) 3!+ 6 ' & #) * ' & **##.
#) * / & **#/ 0 ( */ ) ! 1 b # 0 q. #) * / & **#/ 0!+ */ 3 * ) 3!+ 6 ', * # |q| < 1. +( + /* * /6 1 + * ' * !* / #/ * !
b + bq + bq2 + ... + bqn-1 + ...
+* " ) + & **##, 3 ( # #, ) + b/(1 - q).
3. % %#/ ( '* +# & )#*.* # * %#, * & * ' +*/ ( '* +# a )#* #0 3 2 */ 3 * ) ' ( */ #) ' ( 3. ) ,
a = a0 + 0.a1a2...an... ,
&( a0 - % )#*, 0!+ % ' ) * ( '* +# & )#* a, a1, a2,...,an,... - %#$! 0, 1 , ..., 9. %# ! )#* #0 3 2 */ # (#) * # # ( 3/ #, # %# ! )#* * + * + # (#) * # 0 2 #/.
( !" * ) /" + 0 # (+ '* + |
|
(* + # ( & # & 2 ( '* +# |
& )#* 0 ! # 3 * ) ! # |
|||||||||||||||||||||||||
( */ #) ! # ( 3/ #. 8 #*" (# * )#* #, # 6# # 0 # # 9 + # (. |
, )#* |
|||||||||||||||||||||||||||
|
|
|
|
|
|
|
a0 + 0.a1...an-1an99...9..., |
|
an < 9, |
|
|
|
|
|
|
|||||||||||||
# |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
a0 + 0.a1... |
an-1(an + 1)00 |
...0... |
|
|
|
|
|
|
|
|
|
||||||||
+ ! 2( * 3 ', * |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
a |
|
+ 0.a |
...a |
a |
99...9 = a |
|
+ 0.a |
|
...a |
a |
00...0 + |
|
9 |
+ |
|
9 |
|
+ ... |
||||||||||
0 |
0 |
1 |
|
|
|
|
|
|||||||||||||||||||||
|
|
|
1 |
|
|
n -1 |
n |
|
|
|
|
|
n -1 |
n |
|
|
10 n +1 |
10 n +2 |
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
a |
|
|
+ 0.a |
...a |
|
a |
00...0 + |
|
|
9 |
|
|
|
= a |
|
+ 0.a |
...a |
a |
00...0 + |
|
1 |
. |
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|||||||||||||||||
|
0 |
1 |
|
|
n-1 n |
|
10n+1 (1-1/10) |
|
0 |
|
1 |
|
|
n-1 n |
|
|
10n |
|
||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
12 |
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 3. 0( ! 1 ' # # + * #) * & #0
* # (+ '* + (* + # 2 , * +# */, #, ) 3 * ) / ( */ #) / ( 3 # 9 +
# (.
( ( '* +# ! # )#* # 2 #0+ (# #$#) * # %##, " / + * ( ' 7 0 ( */ + *
" #) * #* ## ( '* +#' ( 3 * ) ! # ( */ #) ! # ( 3/ #. .# * # ) +#( !' (" (
# * 2 #/ (+ " )#*
a = a0 + 0.a1a2...an...
#
b = b0 + 0.b1b2...bn... .
(!+ *
a0 + b0,
(a0 + 0.a1) + (b0 + 0.b1),
(a0 + 0.a1a2) + (b0 + 0.b1b2)
# (. 3 0 )#
(a0 + 0.a1a2...an) + (b0 + 0.b1b2...bn) = c0n + 0.g1ng2n...gnn.
9 ! )#* c01, c02, ..., c0n, ... 3 0 3!+ 6 * ( + *. )# / * & n0, +* )#* c0n,c0n+1,... 3 ( * + */ (# +! #. 8 )#* # 0 c0. ) ( / +*/ & k %#$! gkk, gkk+1, ..., gkn, ...
3 0 3!+ 6 * ( + *. )# / * & nk, +* %#$! gkn, gkn+1, ... 3 ( * + */ (# +! #. 8 %#$ # 0 gk. # 3 0, /+ / */ 3 * ) / ( */ #) / ( 3
c = c0 + 0.g1g2...gn...,
13
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 3. 0( ! 1 ' # # + * #) * & #0
+ / * a + b.
3 0 )# ) 0 — 2 * + +* " ( '* +# !" )#*. #$#) * # %## ( ( '* +# ! # )#* # ()# / */ * ( 6# * +#/:
1.(a + b) + c = a + (b + c) - ** %# #+ * * 2 #/;
2.a + b = b + a - #+ * * 2 #/;
3.( / 3 & a Î — * + ( #+ + * + a + 0 = a - 0 + * 2 ##;
4.( / 3 & a Î — * 6 * + )#* (-a) Î — , ) a + (-a) = 0 - + 0 2 * +!)# #/;
5.(ab)c = a(bc) - ** %# #+ * 2 #/;
6.ab = ba - #+ * 2 #/;
7. ( / 3 & a Î — * + ( #+ + * + 1a = a - (# #%! + 2 ##;
8.( / 3 & a Î —, a ¹ 0, * 6 * + )#* a-1 , ) aa-1 = 1 - + 0 2 * ( #/;
9.a(b + c) = ab + ac - (#* #3 #+ *.
. * ( ! (+ ( '* +# !" )#*
a = a0 + 0.a1a2...an...
#
b = b0 + 0.b1b2...bn...,
( */ #) ! 0 #*# !" * ( 2 9 + # (. + * + a < b * + ( #+ + * ), * # #3 a0 < b0, #3 * 6 * + n ', ) a0 = b0, a1 = b1, ..., an-1 = bn-1, an < bn. .( 2# ) *+ '* + ( '* +# !" )#*,
*/6#"*/ + * +:
10. * # a < b # b < c, a < c - 0# #+ * + * +;
14
com.neevia.http://www version trial Converter Personal Neevia by Created
%#/, 1 4. +*2 # +#/'*( ( ##
11. |
* # a < b, ( / 3 & c Î — * + ( #+ |
+ * + a + c < b + c; |
12. |
* # a < b, ( / 3 & c > 0 * + ( #+ |
+ * + ac < bc. |
&, ) +#( *+ '* +
13.( / 3 & a Î — * 6 * + % )#* k , ) a < k - *# "# (.
#, ) *+ '* + 1-13 ( + + / 2 * + ( '* +# !" )#*, # 2 * + %# !" )#*. ( '7 ! 3 2# 6 ( *+ '* +, #* 6 2 * + —, +! / */ + 2 * + %# !" )#*.
# #0+ * ! %## ( 2 * + #.
( # 1. C A B, C = A È B, C ,
A B.
#*. 1. 35 (# # 2 * +.
( # 2. C A B, C = A Ç B, C ,
A B.
15
com.neevia.http://www version trial Converter Personal Neevia by Created
%#/, 1 4. +*2 # +#/'*( ( ##
#*. 2. .* ) # 2 * +.
( # 3. C A B, C = A\B, C ,
A, B.
#*. 3. 0 * 2 * +.
, B Ì A, A\B B A.
16
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 5. 3 2 #/ 2 * +
#*. 4. # B + A.
2 #* 0 + # ( %## ( 2 * + #, ( + ( '7 3 */ #7 ( #/ 1-3.
* $ , *+/0!+ 6#" 0 #) ! %## 2( * 3 '. .2, #, ) * # B Ì A, A = B È (A\B), #) B Ç (A\B) = Æ, &( Æ - * 2 * +.
'* +# , * # x Î B, x Ï A\B # * ( + , B # A\B # * * ) #. &, * # x Î A, + 0 2 ( #0 (+ ": #3 x Î B, #3 x Î A\B. # 3 0,
AÌ (B È (A\B)).
( & ' * !, * # x Î B, x Î A # * # x Î A\B, x Î A. # 3 0,
(B È (A\B)) Ì A,
) + * * (!( 6# + ) # ( 0!+ 2 $ * + ( ## A # B È (A\B).
5.
( # ! 2 * + #" " #* #.
( # 4. f: X ® Y X Y,
y Î Y x Î X , f(x) = y.
17
com.neevia.http://www version trial Converter Personal Neevia by Created
, %#/ 1 5. 3 2 #/ 2 * +
3 6 + # #, ) ( & " " + ( ## 4 /+ / */ ) * 0+ #/. # * + #, ( # 4 ++
# "3 2 # ".
( # 5. f: X ® Y , X Y
y Î Y x Î X , f(x) = y.
) +#( , ) +0 # ( 0 ) 3 2 # ( * 3 3 2 #.
( # 6. ! f: X ® Y - . " g: Y ® X
f, g y Î Y x Î X, f(x) = y. g = f-1.
# 3 0,
y = f(x)Û x = f-1(y).
#*. 5. 0 # ( 0 ) 3 2 #.
( # 7. ! f: X ® Y g: Y ® Z. " h: X ® Z ,
# f g, h = g °f, h x Î X z Î Z , z = g(y),
y = f(x).
%# * 2 3 2 # 2 0 #* $' z = g(f(x)).
18
, %#/ 12 * + |
19 |
5. 3 2 #/ |
|
#*. 6. 2 3 2 #.
Created by Neevia Personal Converter trial version http://www.neevia.com