How do I communicate to my players that a door is, for the time being, absolutely locked to them?

I have a small dungeon in my campaign, a temple, that is a significant location for the broader story of my world. The players might very well enter this temple pretty early on in their adventuring. There is a door in this temple, however, that must remain securely locked from to all intruders until a much later date – this temple, particularly what lies inside the locked door, will come back as an important location in the future. Ideally, for now this door will evoke mystery and intrigue for my players. However, I am worried that my players will be convinced that the locked door is some type of puzzle. How do I effectively communicate that this door is 100% locked to them, something to be revisited at a later date? How do I stop my players from wasting excessive time guessing passwords and looking for keys?

This is a question that probably fits many tabletop rpgs, but if it matters, we are playing D&D 5e in an pretty standard medieval fantasy setting.

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Pointless, non-singular , absolutely irreducible plane curves over finite fields

We think the following is true:

For all sufficiently large primes $ p$ and all natural $ g \ge 1$ , there exists plane curve $ f(x,y)=0$ over $ \mathbb{F}_p$ which is non-singular, absolutely irreducible, of genus $ g$ and it doesn’t have any rational points.

Is it true?

Is it known?

$\sum u_v$ converges absolutely iff $\sum \log(1 + u_v)$ converges absolutely

I have trouble understanding the following proof of a fact in complex analysis.

Assume $ (u_v)_{v\geq1}$ is a sequence of complex numbers and $ (u_v) \neq -1$ for all $ v$ . Then we have the following Proposition.

In particular I want to understand the estimate $ \frac23|u| \leq\log(1+u)| \leq \frac43|u|$ . I know that for $ |u| < 1$ the power series expansion of $ \log(1+u)$ is: $ $ \log(1+u) = \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n} u^n$ $

Triangle inequality doesn’t seem to help, but how can I derive the estimates?

Uniqueness proof : a = a’ so a is unique. Is the proof absolutely rigorous?

My question deals with uniqueness proofs. For example the proof of the uniqueness of the null set, or the proof of the uniqueness of the identity element in a group.

These proofs are convincing of course , but are they absolutely rigorous?

Is it possible to consider the following objection : when I prove that null-set- 1 and ( hypothetical ) null-set-2 are in fact equal, I prove that the total number of null sets is not equal to 2, but is this the same as showing that the total number of null sets is equal to 1?

How to make totally explicit the logic that is behind uniqueness proofs?

Is this logic questionable?

Find all the $c \ge 0$ for which $\sum_{n=1}^{+ \infty }a _{n}$ is absolutely convergent

We consider: $ $ a_{1}=c-1$ $ $ $ a_{n+1}= \frac{-n}{n+c \cdot \sqrt[n]{ln(n^{9876}+17)}}\cdot a_{n}, n\ge 1$ $ $ $ c\ge0$ $ I want to use Rabbe Test, because then in a simple way it comes out that the series is convergent for every $ c\ge0$ . However I have two doubts: 1) Raabe Test is for $ a_{n}>0$ , but if I do $ r_{n}=n(|\frac{a_{n}}{a_{n+1}}|-1)$ I knew that I must removing minus at $ n$ and then I can leave the module. Hovewer I’m not sure if it’s allowed. 2) If Raabe Test is a good way to do this task I knew only when my series is convergent, but I don’t knew when is absolutely convergent so the more I do not know if Raabe Test is a good idea.