The Empty Set
I kept referring to this as the Null set, but apparently that is something entirely different. It sued to be the same, but the name was taken for a particular purpose.
The Empty set is a mathematical term and it refers to the set that has no members. For the record, a set that contains only 0 is not an empty set, it has an element.
Math has rules about the empty set. Well, about all sets.
the empty set plus any set A is A.
All that the empty set has in common with any set A is the empty set.
And relatedly, the empty set is a subset of any set A.
There are more rules, but I don’t want to think about Cartesian products, Cardinality, etc, so I’ll stop there.
What does that last one mean? Every element from the empty set is part of any set you want to think of. in layman’s terms, you can give whatever characteristics to the empty set that you want.
You my dear readers are an empty set. Or at least I hope you are. There is no reason for you to not be.
Which is why you want to know what I think or why you missed me. Or why you are all 7 feet tall with purple hair. If I were to say “one of my readers is 7 feet tall with purple hair”, that would be inaccurate. But if I say “my readers are 7 feet tall with purple hair”, I’m not actually saying that I have a reader like I am in the first one.
Math is fun!
The Empty set is a mathematical term and it refers to the set that has no members. For the record, a set that contains only 0 is not an empty set, it has an element.
Math has rules about the empty set. Well, about all sets.
the empty set plus any set A is A.
All that the empty set has in common with any set A is the empty set.
And relatedly, the empty set is a subset of any set A.
There are more rules, but I don’t want to think about Cartesian products, Cardinality, etc, so I’ll stop there.
What does that last one mean? Every element from the empty set is part of any set you want to think of. in layman’s terms, you can give whatever characteristics to the empty set that you want.
You my dear readers are an empty set. Or at least I hope you are. There is no reason for you to not be.
Which is why you want to know what I think or why you missed me. Or why you are all 7 feet tall with purple hair. If I were to say “one of my readers is 7 feet tall with purple hair”, that would be inaccurate. But if I say “my readers are 7 feet tall with purple hair”, I’m not actually saying that I have a reader like I am in the first one.
Math is fun!