2. Geometric mean: gn = (a1a2 ... an) (1/n).

3. Arithmetic average: an = (a1+a2+...+an)/n.

4. Square average: qn = √ (a12+a22+...+an 2)/n The formula that these four averages satisfy Hn≤Gn≤An≤Qn is the average inequality.

The essence of inequality.

Add and subtract the same number or formula on both sides of inequality, and the direction of inequality remains unchanged. When both sides of inequality multiply or divide the same positive number, the direction of inequality remains unchanged. (The equivalent coefficient is 1, which is positive when used).

When both sides of inequality are multiplied or divided by the same negative number, the direction of inequality changes.