Are you teaching sets? Some of the stuff that you talk about in set theory is pretty clear – you have a basket { } and you put stuff in it {♥, ✂, ☎, ✿}. No problem.
But what’s the deal with the basket with no stuff in it?
That’s the empty set. It’s written like Ø or simply as the “basket” like this: { }.
But kids might be tempted to write {Ø} – and then they get it wrong. BUT WHY?
The empty set is an object!
Suppose you have four empty sets. Do you have nothing? Nope – you have four containers. Just check your cabinets – I’m guessing you have a handful of empty sets in there with the Rubbermaid® or Tupperware® logo on them.
And {Ø} is an object inside a set.
Supposed you put one inside the other, like this:
This is the same as {Ø}. Would you be willing to put leftovers inside the bigger one while the smaller one is there? It would be something like this:
Instead, wouldn’t you be more likely to remove one empty set from the other and have just Ø and Ø (no curly brackets) like this:
What do you think? Does this help you understand the empty set? Will it help you teach it?
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