Kronecker delta

The Kronecker delta is like a tool that helps us keep track of where things are in a list. Imagine a long list of different things, like fruits: apples, oranges, bananas, grapes, and so on. Now, imagine we want to find out where the apples are in the list. We can use the Kronecker delta to help us.

The Kronecker delta is simply a value that is equal to 1 if two things are the same, and 0 if they are different. So, if we want to find out where the apples are in our list, we can write:

δ(apples, fruits) = 1

Here, δ stands for the Kronecker delta symbol, and apples is what we are looking for in the list of fruits. The Kronecker delta tells us that apples (which is the same as apples) is at the first position in the list, so we put a 1 next to it.

But what if we want to find something that is not in the list? For example, let's say we want to find pears, but pears aren't in our list of fruits. We can use the Kronecker delta to tell us that pears are not in the list:

δ(pears, fruits) = 0

Here, δ tells us that pears (which is different from apples, oranges, bananas, grapes, and so on) are not in our list of fruits. We put a 0 next to it to show that there is no pear in the list.

In summary, the Kronecker delta is a simple tool that helps us keep track of where things are in a list. It is equal to 1 if two things are the same, and 0 if they are different.