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by mden 4429 days ago
I know where you are coming from... but I have started interpreting the word "trivial" (and I don't mean the math meaning of it, e.g. "empty set is a trivial solution") to be a canary of sorts. Once you encounter it and the statement that is supposed to be "trivial" isn't, that means you should backtrack and figure out what insight you are missing to make that statement trivial.

Of course, this kind of depends on the level of the author - some authors don't fully manage to put themselves in the shoes of the reader and take too much knowledge and experience for granted.

2 comments

As soon as I realized this, it actually became quite helpful.

Saying something is "easy" or "obvious" is useful! It may demotivate if done poorly. However with a proper teaching approach it also signals what SHOULD be obvious. If it's not obvious to you yet, it's important to learn and understand why not, and eventually it should become obvious.

If there's any subject which would benefit from interactive textbooks, it's mathematics.

I'd like a textbook in HTML, where when it says "trivial" I can click and expand it to the proof, with relevant references that I can keep going through until I understand how we got there.