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The Algebra, 9 classes, Section IX, INEQUALITY, § 49, Characteristic digital inequality
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   The Theorem 1: If a < b and b < c, that a < c
   The Theorem 2: If before both parts correct inequality to add one and ditto number, that shall get the correct inequality
   The Theorem 3: If both parts correct inequality to multiply on one and ditto positive number, that shall get the correct inequality. If both parts correct inequality to multiply on one and ditto negative number and change the sign an inequality on opposite, that shall get the correct inequality
   The Theorem 4: Inequality with alike sign possible term by term to add. For instance if a < b and , c < d that a+c < b+d.
   The Theorem 5: Inequality with alike sign possible term by term to multiply if their left and right parts - a positive numbers. For instance if a < c, c < d and numbers a, b, c, d - positive, that ac < bd.
 
Задача 24. Positive or negative number a if :
а) 2a < 3a;     б) 0,5a > a;     в) -5a < -4a .
Date:   06-09-2004
Decision: а) a > 0;     б) a > 0;     в) a > 0 .
Date:   06-09-2004
 
Problem 25. Add term by term inequality :
а) 5 < 12 and 7 < 8;     б) 3 < 6 and -3 < -2 ;
в) 5 < 6 and x < z;     г) a < b and x z ;
Date:   06-09-2004
Decision:
а)
   5 < 12
+
   7 <  8
  -----------
  12 < 20
б)
    3 <   6
+
   -3 <  -2
  -----------
    0 <  4
в)
Date:   06-09-2004
 
Problem 26. Multiply term by term inequality :
а) 2 < 3 and 5 < 8;     б) 5 < 7 and ;
в) and ;     г) -4 < -1 and -5 < -4 ;
Date:   06-09-2004
Decision: а)
2 < 3 and 5 < 8
2 · 5 < 3 · 8
10 < 24
Date:   06-09-2004
Decision: б)
5 · < 7 ·



Date:   06-09-2004
§48   §49   §50
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Rubric anecdote
Casual anecdote
(Учительница спрашивает Вовочку, знает ли он Циолковского, Кулибина, Попова?
- А вы знаете Серого, Зубатого и Куню?
- Не знаю, - отвечает ошарашенная учительница.
- Ну так и нечего меня своей бандой пугать.)
The Tutoress asks Vovochku, knows he Ciolkovskogo, Kulibina, Popova?
- But you know the Sulphur, Zubatogo and Kunyu?
- do Not know, - answers the flabbergasted tutoress.
- Well so and nonhis(its) me its gang to scare.
 
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