In an Advanced Calculus course, students were asked to prove $$|a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$$ for $n$ real numbers $a_1,a_2,...a_n$
I am teaching assistant for this course, and one of my students replied like this:
$|a_1+a_2|\le |a_1|+|a_2|$ by triangular inequality.
Then, $|a_1+(a_2+...+a_n)| \le |a_1|+|a_2+...+a_n|$
$|a_1|+|a_2+(a_3+...+a_n)| \le |a_1|+|a_2|+ |a_3+...+a_n|$
Repeating this ,
|$a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$
I gave him a bad grade (5 from 10), so he complained. It is my turn to reply.
- Is the student's proof correct?
- Is the point deduction justified? The professor and I expected the students to use mathematical induction for this proof.
- How can I most clearly communicate the grading rationale to the student in our upcoming conversation? How can I defend the grading policy against student objections?
I posted the question on mathstackexchange too: https://math.stackexchange.com/questions/4083896/grade-on-proving-a-1-a-2-a-n-le-a-1a-2-a-n?noredirect=1#4083901