-, (1). - , - , , - , , -, , , ..
, , .. . ,
A (x > 3)
A x. ( ), - , (.. F { T, F }). - . 1-2.1 . : Ø , , , → , , Å .
(x 1, , xs) s - (s ≥l) , x 1, , xs , - . xi - i (i = 1, , s). -
(x 1, , xs) | á a 1, a 2,..., as ñ, - |
(a 1, , as) .
. , , s ≥ 1
(x 1, , xs) (x 1, , xs) | = | (x 1, , xs) | (x 1, , xs), |
(x 1, , xs) (x 1, , xs) | = | (x 1, , xs) | (x 1, , xs). |
i xi (i = 1, , s),
Ø (x 1, , xs) | = | (x 1, , xs)). |
2.1. . - , 2-1. - . - . 3-8, 3-9, 3-15 3-16 . . , - . 3-8 á x, y ñ , - x 2 +y 2 = 1 (.. -). (x, y): x 2 + y 2 = 1. , . 5) 1 (x): x > 3 , ó- 3.
|
|
, , - , .
= { x | (x)}, (3)
: x, . (3) x = á x 1, x 2,..., xs ñ -. , , , - .
, . -, , , , .
. () ; - M.
( M) (), (4)
, ,
( ) (), (5)
: , - () , . -, () (4), (5) () - .
( M) (), (6)
, ,
( ) (), (7)
: , , - () , . - , () (6), (7) .
12. (): . - . , ( - !):
, . ■
. (x 1, , xs) s- (s ≥ 2); xi i (i = 1, , s). - i = 1, , s
( i M) (x 1, , xs), (8)
( i M) (x 1, , xs) (9)
(s 1)- , x 1, , x i1,
xi +1, , xs. xi (8), (9) , -, , -. , - 1. (.. , - ) . , : , , , , - . , i , t , , ( ): , .. : 1) (, , .) , 2) , -. , , .
|
|
,
( i M) (a 1, , ai 1, xi, ai +1, , as), (10)
, ai Mi xi
(a 1, , ai 1, ai, ai +1, , as) (11)
.
( i M) (a 1, , ai 1, xi, ai +1, , as), (12)
, ai Mi xi, -
(a 1, , ai 1, ai, ai +1, , as) (13)
.
, (. 3-5). = á G, X, Y ñ , . () Y, - . ,
() = { y Î Y | ( x Î ) á x, y ñÎ G }. (14a)
(14a) | , (3). - , y Y. () Y, ( x Î )á x, y ñÎ G .
= á G, X, Y ñ , , - 1() X, - . ,
1() = { x Î X | ( y Î ) á x, y ñÎ G }. (14b)
3.1. . , - , , . , ( -) , , -. .
13. 1- 12: . . , - :
,
, . ■
14. . - , , - , . , - ■
13 14, , - .
1.
( .) | (: ) |
- ( .) | (: ) |
. -, (. 1).
|
|
15. , A, B, C.
( ) , . A B
, C ■
1. . 3 . :
) ;
) , ;
) , ;
) , .
1. 1 ∕ x, {3, 5, 0}
2. 1 ∕ x, {3, 5}
3. 1 ∕ x, {0}
4. 1 ∕ x, { , +}
5. , {5,4,3, 2,1, 0, 1, 2, 3, 4}
6. , {5,4}
7. , {3,4}
8. , {8, 7, 100}
9. , {3,4,!}
10. , {3, 1+ i }■
2. .
1. (x, y): x 2 + y 2 ≥ 2 xy
2. (x, y): x + y ≥ 2 xy
3. (x, n): xn > 1 + n (x 1)
4. (x, y) → (x, y)
5. (x, n): x < n
6. (x, n) (x, n) ■
3. (x, y) x, y,
1. (x, y): y = x 2.
2. (x, y): 2 x + 3 y 1 > 0.
3. (x, y): sin(x + y) = 0.
4. (x, y): y = x 2 + 1 ∕ x.
5. (x, y): y < x 2 + 1 ∕ x.
6. (x, y): y = .
7. (x, y): y = ■
4.
1. ( )[ () (x)] º ( ) () ( ) (x)
2. ( )[ () (x)] º ( ) () ( ) (x)
3. ( )[ () (x)] º ( ) () ( ) (x)
4. ( )[ () (x)] º ( ) () ( ) (x)
5. ( )[ ()→ (x)] º ( ) ()→( ) (x)
6. ( )[ () (x)] º ( ) () ( ) (x)