RATIONAL NUMBERS, PROPERTIES, OPERATIONS
Additional Properties of Rational Numbers
1) Law of Tricotomy: For every a,b,\(\in\) Q any one of the following is hold.
i) a<b ii) a>b iii) a=b
This property of Rational numbers is called 'Law of Tricotomy
2) Transitive property: For every a,b,c \(\in\) Q and if a>b and b>c then a>c
This property of rational numbers is called 'Transitive property'
3) Density property: Between two rational numbers infinite number of rational numbers are there. This property of rational numbers is called Density property
4) i) If a,b \(\in\) Q and c is positive integer and if a>b then (i) a+c > b+c
ii) If a,b\(\in\) Q and c is negative integer and if a>b then (i) a - c > b - c
5) i) If a,b \(\in\) Q and c is the positive integer if a>b then a.c>b.c also \(\frac{a}{c} > \frac{b}{c}\)
ii) If a,b \(\in\) Q and c is negative integer if a>b then a.c<b.c