Made a couple of Java assignments

Manitou and I met yesterday and made a couple of Java assignments which were overdue. We implemented a Heap using the Locator pattern and a Vocabulary using a Trie — it was a very good learning-experience to actually implement these ADTs instead of just talking about them.

We also talked about other things — we met at 14:00 and went home again at 23:30 so there was plenty of time :-) One of the things we discussed extensively was, that he had a book, which said, that the set of all subsets of the empty set, which is denoted 2, is {∅, {∅}}. I don’t believe that this is true — the only subset of ∅ is ∅ itself, so I would say that 2 = {∅}. If 2 = {∅, {∅}}, then that would imply, that ∅ ∈ ∅ which is clearly false, as the empty set is empty. We’ll ask Jørgen Hoffman-Jørgensen about it — he should know as he’s our teacher in Probablility Theory.

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