eli5 Why is the empty set a subset of any set?
In: 2
It’ll be easier to explain it with the notion of **superset**.
A set *bigbag* is a superset of *smallbag* if you can obtain *bigbag* by adding objects to *smallbag.* In particular, *bigbag* is always a superset of the empty set, because if you have the empty set, you can just add all the objects of *bigbag* to obtain *bigbag*
The other way around, *smallbag* is a subset of *bigbag* if you can obtain *smallbag* by removing objects from *bigbag*. In particular, the empty set is always a subset of the bigbag, because you can start from *bigbag* and remove all the objects.
If that doesn’t feel intuitive too you, it’s probably you don’t fully grasp that the empty set is a set. It is kind of weird said like that, but using bags: the empty set is a bag with nothing in it, but it’s still a bag.
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