. , , ,

,,,

1. n- , . , e, - , , , , .

S l2 , . S :

1=(1, 0, 0, ..., 0, 0, ...),

2=(0, 1, 0, ..., 0, 0, ...),

,

n=(0, 0, 0, ..., 1, 0, ...),

.

n (n¹m) Ö2. {i} . S e- e<Ö2/2.

l2

x=(x1, x2, ¼, xn, ...),

:

| x1|£1, | x2|£1/2, ¼,| xn|£1/2n-1, ...

( ) l2. . .

e>0 . n , 1/2n-1<e/2. x=(x1, x2, ¼, xn, ...)

x*=(x1, x2, ¼, xn, 0, 0, ...)

.

r(x,x*)=£<1/2n-1<e/2.

* x*=(x1, x2, ¼, xn, 0, 0, ...) ( n- ). * e/2-. e- . .

: "e>0, n , 1/2n-1<e/2.

"xÎ: x=(x1, x2, ¼, xn, ...)

x*=(x1, x2, ¼, xn, 0, 0, ...) x*Î. r(x,x*)<e/2. x**: r(x*,x**)<e/2.

: r(x,x**)£r(x,x*)+r(x*,x**)<e/2+e/2=e.

* x*=(x1, x2, ¼, xn, 0, 0, ...), e/2-. e- , r(x,x**)<e.


1. n- , . , e,

 

 

 

! , , , .
. , :