The set of Mammals is a subset of the set of Animals.
The set of Cats is a subset of the set of Mammals, and therefore also a subset of the set of Animals.
The progression of subsets is important to us. We have a tendency in a definition to make a mention to something more general.
We might say, a tiger is a large cat with orange and black stripes. This tells us that tiger is a subset of cat and we add to this that itd size is large and its appearance includes stripes that are black and orange. This is probably enough for you to recognize a tiger when you see it in the zoo.
Thinking about hierarchy changes your thinking. For example, while reading a paragraph in foundations of mathematics, you come across the idea that a sentence has a value of true or faults and a formula is something that is true or false depending on your choices of vsriables.
This will make you think okay sentence and formula go in a set and you might ask yourself are there anything else to fit in this set and then you ask yourself what is the general name for the set just like the general name for a set with Lion, Tiger and Leopard was Cat.
Rob Sterling 