Despite having a lot due on Friday, I was able to get through it all and finish the first assignment. My main issue turned out to be with the last question (the binary substring question); I did the proof almost entirely in English, and originally tried to prove it by starting at a smaller string and showing any combination of larger strings would have the same property, but after consultation with Dan this proved to be more difficult to do convincingly. I ended up going backwards; showing that if a given string has the property, the next smallest string ending with the same digit also has the property.
It was interesting for me to learn that proofs written entirely in a natural language are not only acceptable, but in some cases preferable to those heavily relying on mathematical notation. I can see why, too; writing in a natural language forces you to express your thinking very explicitly and can expose you to holes in your reasoning.
I've been mostly following the lectures, but I need to do some practice for the test coming up in two days. I plan to go through the lecture exercises and write some past tests as soon as possible!
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