# Wild About Math!Making Math fun and accessible

1Apr/083

## Proof: all April fools’ jokes are interesting

Do you get inundated with April fools' jokes every year? They all seem interesting, don't they? Have you ever wondered if someday you'll encounter an uninteresting April fools' joke? As it turns out, all of them are interesting. Here's the proof.

This will be an indirect proof. We'll assume that there are some uninteresting April fools' jokes and we'll show a contradiction.

1. Let S be the set of uninteresting April fools' jokes.

2. Since we're assuming that there exists at least one uninteresting April fools' joke then we assert that S is not the empty set.

3. By the well ordering principle, every non-empty set of April fools' jokes contains a least interesting element.

4. Let L be the least interesting element of set S.

5. So, there exists a least interesting April fools' joke. Well, that's pretty interesting.

6. So, we've encountered a contradiction. Thus, our original assumption, that there are uninteresting April fools' jokes, is incorrect. Thus, all April fools' jokes are interesting.

QED