Hi,

I know many of you have not written proofs before, although our course is not proof-based, we do want us to get into the habit of giving reasons. This a natural thing when you are talking to someone.

You say, 'I like orange', they ask 'why?', you say, 'I don't know, I just do'. That's fine in life, since many things cannot be explained. That would be funny when you do math, where math is one of the few lucky places where reasoning works.

You want to write a proof as if you are explaining something to yourself. Indeed, yourself, not someone unknown. More precisely, you want to explain it to your future self. That means

• Explain what you are doing (i.e. restate the problem, before solving it)
• Be gentle. Don't say, 'it is obvious', otherwise if you would feel stupid if you don't get it.
• Be a little bit verbose. You don't want to assume your reader to know/remember everything (but you don't want to assume they know nothing, that would be condescending.)

Feel free to make mistakes. If you are in a straight-jacket, that would not be fun at all (and you won't learn). Most of the idea may not work, but as long as 1 out of 10 works, that's something.