My Discrete Mathematics book talks about the proof of why null set is the subset of every non-empty set. It has raised some questions in my head.
Firstly, Why? I mean why will we want to make simple, intuitive things so complicated. I mean why is there need to say tht non-empty set contains an empty set? We can see that a non-empty set has elements and combination of atleast one of them will be a subset of the main set which makes perfect sense. But why will we need to bring up the whole counter intutive idea of null set being a subset? Same question about the set being the subset of itself.
What I am looking for is that if somebody can help me understand the purpose and importance of doing so.