Derived set (mathematics)

Let's imagine that you have a group of toys. You can play with them, arrange them, and take them away as you wish. Now, let's say that you have a special set of toys that you can't play with directly. These toys are called "derived toys."

Derived toys are special because they are made up of other toys in the group. In other words, they are created by combining or changing the toys you have. For example, if you have a toy car and a toy truck, you can combine them to create a new toy: a car-truck. The car-truck is a derived toy because it is created by combining other toys.

Similarly, in math, a derived set is a set that is made up of other sets. But instead of playing with toys, we are talking about numbers, functions, or other mathematical objects. Just like with the toys, we can combine or change these objects to create new ones.

For example, let's say that we have a set of numbers: {1, 2, 3, 4, 5}. We can create a derived set from this by taking all the numbers that can be obtained by subtracting two different numbers in the original set. In this case, we get {1, -1, 2, -2, 3, -3, 4, -4}. This is our derived set, and it is made up of numbers that were created by subtracting two numbers from the original set.

In summary, a derived set is a special set that is made up of other sets or mathematical objects. Just like with toys, we can create these derived sets by combining or changing the original objects in different ways.