I don’t see any reason why more competent people would prefer omission of a key step in a proof with remark “left to readers as an excercise”. If you want to save time, you can surely skip it while reading. Why shall the author make the choice for the reader?
Especially in math, even textbooks which are intended to present complete overview of some subject have these excercises to the reader. I like to read books from the beginning to the end, but this is exactly what makes it impossible for me to do with math books. It can be refreshing to stop reading at some moment and have to think about some detail, but to do it repeatedly, knowing that I am losing time trying to figure out something which could be explained on two lines, is frustrating. I read books and papers because I want to get the information as efficiently as possible, not because I want to eventually rediscover it for myself. Not much to do with competence, I believe.
Added: I also find “excercise to the reader” mildly offensive, as the author is saying that it is trivial for him, but not for the readers, who should improve their skills by making the excercise. Such sentences aren’t surprising in undergraduate course textbooks, but when the audience are competent people, it seems inappropriate.
I don’t see any reason why more competent people would prefer omission of a key step in a proof with remark “left to readers as an excercise”. If you want to save time, you can surely skip it while reading. Why shall the author make the choice for the reader?
Especially in math, even textbooks which are intended to present complete overview of some subject have these excercises to the reader. I like to read books from the beginning to the end, but this is exactly what makes it impossible for me to do with math books. It can be refreshing to stop reading at some moment and have to think about some detail, but to do it repeatedly, knowing that I am losing time trying to figure out something which could be explained on two lines, is frustrating. I read books and papers because I want to get the information as efficiently as possible, not because I want to eventually rediscover it for myself. Not much to do with competence, I believe.
Added: I also find “excercise to the reader” mildly offensive, as the author is saying that it is trivial for him, but not for the readers, who should improve their skills by making the excercise. Such sentences aren’t surprising in undergraduate course textbooks, but when the audience are competent people, it seems inappropriate.