. , > () < () . > B C > D ( < B C < D) (), > B C < D ( < B C > D) .
. : 12 3 > 10 ; 12 + 14 < 15 . , , :
(2 < 3) Ù (5 < 3) ; (3 < 5) Ú (1 + 1 > 3 + 1) .
£ = < ,
.. £ Û ( < B) Ú ( = ), ,
(2×4 + 15) × 2 £ 35 + 19 .
< < < < . , . , (25 < 18 + 17 × 2) Ù (18 + 17 × 2 < 100). Ÿ : 25 < 52 < 100. , (<, >) :
1. (" ) [ ],
(" ) [ ];
2. (" , )[ < Þ ],
(" , )[ > Þ ];
3. (" , , ) [ < Ù < Þ < ],
(" , , ) [ > Ù > Þ > ].
13 , , .
13 x y:
1) , x = y, x > y, y > x;
2) (" , )[ x < y Û y x > 0];
3) (" , )[ x > 0 Ù y > 0 Þ x + y > 0 Ù x × y > 0].
, y > x x < y . > < .
1)-3) x, y, a, .
1. (" x, y, a) [ x < y Þ x + a < y + a ].
. x < y Û y x > 0Þ (y + a) (x + a) = y x > 0 Þ
Þ x + a < y + a. x a < y a.
2. (" x, y, a, ) [ x < y Ù a < Þ x + a < y + ].
. x < y Þ y x > 0, a < Þ > 0.
( ) + ( ) = ( +) ( +)> 0 Þ + < +.
3. (" , , > 0) [ < Þ < ].
.
< Þ > 0 Þ ( ) > 0 Þ > 0 Þ > Û < .
|
|
4. (" > 0," > 0," > 0," > 0) [ < Ù < Þ < ].
. < Ù > 0 Þ ( )× > 0 Û < .
< Ù > 0 Þ < . ( < ) Ù ( < ) Þ < Û < .
5. (" , )[ < Þ > ].
. < Þ > 0. = ( ) ( ) > 0 Þ > .
6. (" , , < 0) [ < Þ > ].
. < Þ < Þ > , .. > .
7. (" , Ù 0 < < < < 0) [ < ].
. = , > 0 > 0, > 0 > .
. , , . , 2 + 3 ; 5 + 18; 4 9 . . , , .
. , , , . . , .
, .. , . , .
(), (, ) . .
.
1) : + .
(¥,1) (1, 6) (6, +¥).
2) . +10 0 Þ 10,.. [10, ¥).
3) , , , , N.
4) 5 + 5 + 10 .
. , , .
, ( + )2 ( 2+ 2 + 2) R.
R \{0}.
.
, . , . , , .