How to resolve grading dispute between TA and Lecturer? On a math exam recently, the students were asked to use the definition of a limit of a sequence to prove that the sequence given by 3n/(3n+5) converges to 1. Given a positive number Ɛ, the definition requires proving the existence of some number N such that if n>N then |3n/(3n+5) - 1|&lt;Ɛ.

As a consequence of the definition, once a sufficiently large N is found, any larger value of N will also suffice. Many students set |3n/(3n+5) - 1|=5/(3n+5)&lt;Ɛ and solved for n to find N = (5-5Ɛ)/(3Ɛ). However, the professor decided to include an extra step: 5/(3n+5) &lt; 5/n &lt;Ɛ, which leads to another sufficient value N = 5/Ɛ.

Although most students gave a correct proof (consistent with the definition in their book), the lecturer took off points because they didn't find the "best" value of N. The lecturer claims that the author would have used some (unnecessary) inequalities to find the "better" N, which is probably true.

When students complain about losing points, I tell them that their answer is correct and that they should seek full credit for their work. The lecturer suggests that I am putting the students in a position in which they may "pick a side" and that ultimately the lecturer is in charge.

Who's wrong here?

Update: I was not notified about the lecturer's decision to remove points until after I gave the midterms back to the class. Once students started asking me about the missing points, the only written justification left by the lecturer was "not best N."

By "best N," the lecturer was referring to the N value found by using the additional inequality 5/(3n+5) &lt; 5/n &lt;Ɛ. By "best," he does not mean "smallest" (and by definition, there is no largest N).
The nature of the dispute makes this problem difficult.

As a mathematics (BS) and computer science (MS, PhD) student I have done numerous exercises that required proof of the existence of a natural number N such that for all n>N some inequality is true. In addition to limits in mathematics, they show up in computational complexity analysis of algorithms.

Every time I have done one of those exercises I have picked a value of N that made the proof as simple and clear as I could. Often, I was aware of a smaller value of N that would have required a longer proof. I have never been marked down for picking an unnecessarily large value of N.

Any finite value N, no matter how large, such that the inequality is provably true for all n>N is equally good. That is an important aspect of these definitions, something the students should understand and apply.

If smallness of N were going to be a grading factor, despite its irrelevance, it should have been announced in advance.

That said, it would have been better for the OP to discuss the matter privately with the professor, and perhaps with more senior professors. The OP should not encourage protests directly, but should state the professor's decision and recommend that follow-ups be forwarded directly to the professor or offer to forward them on the students' behalf.