I think the problem here really is that permutations are defined as bijections, which is rather unintuitive. Now even though I learned that in my undergraduate

I think the problem here really is that permutations are defined as bijections, which is rather unintuitive. Now even though I learned that in my undergraduate curriculum I already forgot about that again. Now think of it as a sequence and you get something like this: {(aᵢ) i∈[1..N] | aᵢ∈1..N, ∀i,j : aᵢ ≠ aⱼ}. Probably already easier to understand. Or leave it off totally. Formal mathematical definitions don't make sense when they are harder to understand than words and when you do not use them actually later on.