Max–min inequality

Max-min inequality is like a friendly competition between numbers where we want to find the smallest and the biggest numbers from a group of numbers. Imagine you have a bunch of friends and you want to find out who is the tallest and who is the shortest among them. This is what the max-min inequality is all about.

In math, we use the symbol “≤” to represent this inequality. The sign looks like two lines, where one line is below the other. This sign means “less than or equal to.” For example, if we have two numbers, say 5 and 10, we can write 5 ≤ 10, which means five is less than or equal to ten.

Now, let's take it up a notch. Suppose we have a set of numbers, say 3, 5, 7, and 10. We can use the same inequality sign to compare the smallest and the biggest numbers in this set. We use the ma–min inequality formula to do this:

min number in the set ≤ average of the numbers in the set ≤ max number in the set

In our example, the smallest number is 3, and the biggest number is 10. The average is (3+5+7+10)/4 = 6.25. We can check if the max-min inequality holds true in this case:

3 ≤ 6.25 ≤ 10

So, the smallest number in the set is less than or equal to the average, which is less than or equal to the biggest number in the set.

The max-min inequality is a useful tool in math because it helps us find the range of values that a set of numbers can take. We can use it to compare different sets of numbers and find out which set has the smallest or the largest possible value.