The permutation notation required some mental adjustment for me. Exactly as you said, my mind wants to see it as where the numbers should go (which makes me see (1,2,3) as doing nothing). I had to work through the examples to get it to gel.
The answer to exercise #1 was kind of obvious, but I was a little surprised by the answer to #2.
great work on explaining the topic! if i could add: on explaining (1 2 3)(1 2 3), if you draw 2 sets of arrows over 3 lines, it'll instantly clear that why the result is (1 3 2).
The permutation notation required some mental adjustment for me. Exactly as you said, my mind wants to see it as where the numbers should go (which makes me see (1,2,3) as doing nothing). I had to work through the examples to get it to gel.
The answer to exercise #1 was kind of obvious, but I was a little surprised by the answer to #2.
Good post. Looking forward to more!
great work on explaining the topic! if i could add: on explaining (1 2 3)(1 2 3), if you draw 2 sets of arrows over 3 lines, it'll instantly clear that why the result is (1 3 2).