There's a running Abstract Algebra joke among some of my friends and I that goes: "Oh, just take the canonical bijective homomorphism and show it's well-defined."

I guess one or more of the following is true:

- It's not really that funny.
- It's only funny late at night.
- You have to be there.

Regardless, the reason it's funny is that this is sufficient to prove almost everything. It sounds like you're giving a lot of information, but you actually could be talking about almost any abstract algebra problem, linear algebra problem, or computatiblity/complexity theory problem.

During first term, some people would say, "Oh, the problem's easy. Just find a bijective homomorphism..." Alas, that is the problem! I'm probably guilty of saying something like this before. The key is that if you haven't written up a proof, you haven't proved it. You may have a road map, or a conceptual understanding, but it's still not a proof. You don't know where the pitfalls lie until you write it out step by step.

Here is a chart of excellent buzz-words you can use to confuse me. Construct a sentence using a few of these, and I won't know which of my classes you're even talking about. Alternatively, I recommend The proof is trivial! for all your pseudo-proof needs.