During the course of the weekend I spent considerably more time thinking about null sets than I ever have before. I’m not sure if someone can be a null set fetishist, but if they can, I think the person who crafted the latest round of my homework is. There was a whole lot of null set used in strange and (to me) unusual situations.Now I was never a good math student, so some of this probably won’t be new to those of you who were. Oh, if you’re planning on struggling through the boring math stuff to make it to the funny conclusion at the end of the post…just stop reading. I didn’t have the kind of weekend that encourages humorous antidotes. This is straight-up set theory mathematics from the streets, yo.
First off, evidently some people get their panties in a bind if you casually refer to the empty set as the null set. I’ve always assumed that the two names are interchangeable…not so, say mathematicians worried about measurement theory (there is such a thing as measurement theory?) Evidently the empty set is different from the null set being that the null set is not unique where as the empty set is. In set theory we use the empty set. And it’s the empty set, not an empty set….because it’s unique. This is because in set theory two sets are equal if they contain the same elements. All empty sets contain exactly the same elements (which is none) so they are all the same set, which is to say that there is only one of them (welcome to how I spent my weekend). Also, don’t get me started on the difference between equals and equivalent.
Another important thing to wrap your head around is that the empty set is not the same thing as nothing. The empty set is something; it’s just an empty something. It’s best not to think of sets as collections. If you think of them as collections you’ll be tempted to think of an empty collection as no collection. It’s better to think of sets as bags. If you have stuff in your bag then you have a collection in a bag. If you have nothing in your bag, then you still have a bag. You could have lots of empty bags if you wanted to. You could count them. Heck you could even put an empty bag inside another empty bag. But then the one of the bags wouldn’t be empty any longer. It would contain the empty set.
Throw in the power set of the empty set and Cartesian products of two empty sets and you’ll have my Saturday. I think I might need another weekend to recover from the last one…
4 comments:
"And it’s the empty set, not an empty set….because it’s unique."
Does that mean you're sticking a bag inside itself?
"Does that mean you're sticking a bag inside itself?"
I think this is where math breaks down.
As soon as you put a bag in a bag the first bag is no longer empty, it has something in it, therefore it is not the same as an empty bag.
So, they're the same until they're different.
Perhaps the empty set can be a bag with infinite linings, and once a lining is removed it becomes a new bag that is different from the first in that it doesn't have any linings?
Then the first bag is placed in the second bag and there doesn't have to be any duplication and state-changing. Just, you know, a Bag of Holding.
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