Why Set Theory is irrelevant when discussing Nested Hierarchy

When talking about set theory any sets and subsequent subsets, apart from nested hierarchy, you can have items from one set by included with items from another set on the same level.

With set theory in general anything can be a set. Just put whatever you want in {} and you have a set. Or if you can't find {} just declare what you want to be in a set. Then all subsets are just that set and/ or that set minus any number of items.

For example with Zachriel's paternal family tree I can make a set of {Sharif Hussein bin Ali, Abdul Ilah,Faisal}. A subset would then be {Sharif Hussein bin Ali, Failsal}. It is a valid set and it is a valid subset. However neither make sense in a nested hierarchy.

In a nested hierarchy we can NOT have two sets on the same level that contain items that can exist in either set. Also all subsets must be strictly contained within the set above it.

In nested hierarchy each set and each level are specifically defined by several criteria. This is done such that a person can pick an item from one set, hand it to another person, and from the specifications be able to replace the item in its original set.

That is why when you are talking about nested hierarchy and someone tries to divert the attention to set theory they are up to nothing but deception.