Finitary relation

Let's imagine you have a bunch of toys, and you want to organize them in different ways. One way is by their color: you group all the red toys together, all the blue toys together, and so on. Another way is by their size: you put all the big toys together, all the little ones together, and so on.

Now let's say you have a lot of toys, and you want to compare them to see which ones are similar to each other. For example, you might ask yourself which toys have a similar shape. To do this, you need to define a "finitary relation" between the toys based on their shape.

A finitary relation is a way to group things together based on a specific attribute or characteristic. For example, if you want to group toys based on their shape, you might define a finitary relation where two toys are "related" if they have the same shape. So a round ball and a round balloon would be related, while a square block and a round ball would not be related.

The important thing about a finitary relation is that it only looks at a finite set of attributes or characteristics. For example, you might define a finitary relation based on the color and shape of a toy, but not its size or material. This makes it easier to compare and group things together, because you don't have to consider every possible aspect of each toy.

In summary, a finitary relation is a way to group things together based on a specific attribute or characteristic, looking only at a finite set of those attributes or characteristics. It's like organizing your toys based on their color or size, but with a more specific focus on one aspect at a time.