7.
7.1. . .
7.2.
7.3. .
7.4.
7.5. .
7.6. .
7.7.
7.8.
7.9.
.. IV, 4.1 4.4 .71-82
., . ? I . 25-44, I .45-76, II . 77-98
1. ?
2.
3. ( )
4., .
5. ?
6,
7.
8. ,
9.
10. ( x<0).
. .
, , , , . , . R, .
I. . b , + b, , :
I.1. a + b = b + a, a,b R.
I.2. a + (b + ) = (a + b) + , a,b,c R.
I.3. , ,
a R + 0 = .
I.4. a R ,
-, + (-) = 0.
+ (b), , b R, b b.
. . b , ab (a b), , :
II.1. ab = ba, a, b R.
II.2. (b) = (ab)c, a,b, R
II.3. , 1, R 1 = .
II.4. , a -1 , = 1.
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, b : b /b.
III. :
a,b,c R ( + b) = ac+bc
IV. . . . b
: < b ( " b"), , , b > ( "b "), > b, , , b < . , :
IV1. . <b b < , < .
IV2- < b, + < b + .
IV3. > b > 0, > bc.
. ≤ b, b ≥ , , < b, = b.
IV2 IV3 , : b, , , < b, , < < b. , a = a, b = b c < b, 2a<a + b<2b,
< < b, . . .
.
V. . X Y , X Y x≤y, , x≤a≤y, X Y ( .7.1.)
. 7.1.
, . .
7.1.
, I-V, , , .
. , , , , , I-V.
() , (.. 7.1.(2))
. 7.1. (2)
, . < b ( b > ) , b ( b ).
, +∞ ∞ , , R. -∞< < +∞.
R, +∞ ∞, ( )
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R ∞ ( ), ∞ . +∞, ∞ ∞ , , .
R. a , b , ≤b.
[, b] = {: , ≤x≤b}
,
(a,b) = {: , < < b}
,
[, b) = {: , ≤ < b},
(,b] = {: , < ≤b}
, . b , , < < b, . b , ≤b, b , .
7.1(2).
U(a, ε) = (a - ε, a + ε) ( .7.1(3)
. 7.1(3).