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( # 1. X Y ,

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, , , Õ 1, 2, ..., n, ....

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.

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!" 1 +.

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, %#/ 2 3. ) 35 (# # *) !" 2 * +

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X = {x1, x2, ..., xn, ...}.

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X¢ = {xn1, xn2, ..., xnk, ...}.

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3.

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n=1

# ( 2, ) X /+ / */ *) !.

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# ( * ) 35 (# / & 2 * +, + ' # ( * ) /( +!' 1 * ( + * #

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, %#/ 2 3. ) 35 (# # *) !" 2 * +

X1 = {x11, x12, ..., x1n, ...},

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...........................................,

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........................................... .

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(2)

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# ( * + !" + 4, * x13, x22 # x31. (. ) ( k- 7 & )#* # 1 !, * # ( * +

!" + k + 1, * x1k, x2(k-1), ..., x(k-1)2, xk1. 4 ( ( 2 % ** )#* #/ 3 * ) . # & )# */

* ( + *

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x11, x12, x21, x13, x22, x31, ..., x1k, x2(k-1), ..., x(k-1)2, xk1, ...

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. # # 2 ( / ( 0 * + *) * # 2 * + %# !" )#*. 4 ( 3 0 ) 2 * + +* " % !" )#* ) 0 Ÿ, 2 * + +* " %# !" )#* - ) 0 –.

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3. – # .

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, %#/ 2 4. *) * 2 * + ( '* +# !" )#*

. .2( +* & 0 #, ) 2 * + Ÿ +* " % !" )#* *) 35 (# # *) & 2 * + Õ, + 6 & 2 * + #% !" % !" )#* # 2 * + {0}, * * /6 & #0 /.

- $# *# n Î Õ # 3 0 )#

2 * + –n + 6 2 * + Ÿ # 1 *) . 2 * (, ) 2 * +

¥

– = UQn

n=1

*) *) 35 (# # *) !" 2 * +, ) ( 0!+ 3.

4. ! " "

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, %#/ 2 4. *) * 2 * + ( '* +# !" )#*

a2 = 0.a21a22...a2n...,

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........................................... .

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bn. .( 2# % ** & #) .

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/ %#$ bn ( */ #) ' ( 3# b + n-' %#$ ann ( */ #) ' ( 3# an + n-' * ) (4). .( 2# & #) * + # b * )#* # + * ( + * # (4) # 3 (# */, ) b + # ( #0 )#* + (4). # 3 0,

( '* +# )#* b Î —0 )#* + * ( + * # (4), ) #+ )# ( 6 # *) * # 2 * +

—0.

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1. #

! * # +* * & # * ( + * ', + ', + ) * * #, *$# # ( 2

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+ * +. .#+ ( 1 +# + * ( 6 ' .

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+ 2( #. ( / 36 / * 0( , # + * ## ( +, 1 #" (# */ ( 0!+

1 ( * ! # 1 1 * (* + #.

1. #* a (* +# 3 * ) ' ( */ #) ' ( 3

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, %#/ 3 2. #%! # & # 2 * +

(2) a = a0 + 0.a1a2...an... .

9 )#* a0 2 3! 2# !, + #+ * ) * + ( #+ + * + a ³ a0 ³ 1,

#+ ) 6 * +# ! ( / n = 1.

* # # /, ) a0 < 0, + 2( # ! 1 * +# */ ) +#( !.

. ( 2#, ) a0 = 0. %#$ a1 2 3! 2# ', + #+ * ) * + ( #+

+ * + a ³ 0.a1 ³ 0.1, #+ ) 6 * +# ! 1 # n = 2. ( + , a1 = 0.

* # a0 = 0 # a1 = 0, %#$ a2 2 3! 2# ', + #+ * ) * + ( #+ + * + a ³ 0.0a2 ³ 0.01, #+ ) 6 * +# ! 1 # n = 3. ( + , a2 = 0.

. ( 2#, ) * 6 * + # 7 )#* k , ) %#$ ak 2# . &( * + ( #+

+ * +

a ³ 0.00...0ak ³ 0.00...01,

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3 0, * # + (* + ## (2) a0 = 0, +* %#$! ak, k Î Õ, + ! , 1 0 ), ) a = 0. , 1 ( 0 .

2. $

2 ! # # # 2 * + )#* + ' *# — * 2 0 # [a, b],

[a, b] = {x Î —: a £ x £ b},

# + ! (a, b),

(a, b) = {x Î —: a < x < b},

2 2 ) ! 2 * + [a, b) # (a, b], ! 2 0+ 0 # # # # + #,

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