# Properties of the Numerical Inequalities

For any real numbers `a, b, c, d` is used the following properties:

- If `a>b`, then `b<a`.
- If ` ` ` ``a>b` and `b>c`, then `a>c` (
**the****transitive property**). - If `a>b` then `a+c>b+c`.
- If `a>b` and `c` - positive number (`c>0`), then `ac>bc` (if the both parts of correct inequality to multiply by the same positive number, then we obtain correct inequality)
- If `a>b` and c - negative number (`c<0`), then `ac<bc` (if the both parts of correct inequality to multiply by the same negative number and change the sign of the initial inequality in the opposite, then we obtain correct inequality).
- If `a>b` and `c>d`, then `a+c>b+d` ( if two correct inequalities add termwise, we will obtain correct inequality).
- If `a, b, c, d ` - positive numbers and `a>b` and `c>d`, then `ac>bd` ( if the correct inequality of same sign to multiply termwise, the left and right parts of which are positive numbers, we will obtain correct inequality).
- If `a>b` and `c<d`, then `a-c>b-d`.
- If `a>b>0`, then `1/a<1/b` .
- If `a>b>0`, then `a^n>b^n` for any naturall `n`.