Fréchet inequalities

Fréchet Inequalities are like rules that explain how distances between things can be measured. Imagine if you and your friend are standing far apart, and you want to know how far you are from each other.

First, you can use a ruler to measure the distance between you two. But what if you both move diagonally or in circles? The ruler won't work anymore, and you need to use something called a Fréchet inequality to measure the distance between you two.

Fréchet inequalities are like shortcuts that help you measure distances between things that move around. These inequalities say that the distance between two points is at least equal to the distance of the longest path connecting those points, even if that path doesn't follow a straight line.

For example, imagine a little snail trying to crawl from one end of a long stick to the other. The snail might not crawl straight across, but instead, it might crawl up and down the stick before reaching the other side.

The Fréchet inequality would say that the shortest distance between the two ends of the stick would have to be at least as long as the longest path the snail could take. This might seem a little confusing, but it helps us measure distances between things that don't have a straight line connecting them.

In summary, Fréchet inequalities help us measure distances between things that move around or don't have a straight line connecting them. They provide rules to make sure we measure distances accurately, even if the path connecting two points is crooked or twisted.