Filtered algebra

Imagine you have a big bucket of marbles. Some of these marbles are bigger than others, and some are the same size. You want to organize them in a certain way but you don't want them to mix together. So now you're going to use a filter to sort them.

A filter is like a sieve or a strainer that you pour your marbles through, except it separates them by size. You pour your marbles through the filter and it sorts them into different sections based on their size.

Now, imagine that each section of marbles that came out of the filter is a set. For example, all of the big marbles would be one set and all of the small marbles would be another set. Each set has certain properties and characteristics that make them different from each other, but they are all related because they came from the same big bucket of marbles.

This is kind of like filtered algebra. You start with a big set of numbers and you use a filter to separate them into smaller sets based on certain characteristics. Each smaller set has its own unique properties and characteristics that make it different from the other sets, but they are all still related to the original set of numbers.

Filtered algebra is a way of studying these filtered sets and understanding how they relate to each other. It helps us to better understand the properties and characteristics of different sets of numbers and how they apply to different situations.