## What should happen when a player does not follow his class at all? (i.e. plays his role badly)

I have a player who created a Druid and is mostly playing like a barbarian in combat and like a rogue the rest of the time.

This means he kills animals, does not care for plants, does not use his magic even when someone could use Cure Wounds… (although that last one is certainly okay for a neutral character.)

And when in the presence of an NPC that looks rich, multiple attempts to steal as much as possible from it (like a level 1 character should steal from a cloud giant…)

What would you do in this situation? I’m playing 5e and am allowing all extensions so the characters can multi-class. On my end, I was thinking to force him to choose another class once at level 2. Would that be wise? I think that would be much more likely to teach him a lesson rather than letting him continue as this barbarian/rogue under the disguise of a druid…

To answer the first comment fully:

PHB p64. under Power of Nature

Druids revere nature above all.

So being the first to kill everything, including animals, seems quite contradictory to the class already… (were he evil, I could understand that he like monstrosities, and not “regular” animals, but that is not the case here.)

PHB p64. under Preserve The Balance

Already the title sounds like a Druid seeking just gold and gems and other riches is not going to help much in preserving the balance…

[…] Druids oppose cults of Elemental Evil and others who promote to the exclusion of others.

Gold and gems could be viewed as promoting the Earth Elemental.

Druids are also concerned with the delicate ecological balance that sustains plant and animal life, and the need for civilized folk to live in harmony with nature, not in opposition to it.

This re-enforces my first excerpt.

PHB p65. under Creating A Druid

When making a druid, consider why your character has such a close bond with nature.

I will say, Barbarian are considered to be close to nature as well… so a barbaric fighting aspect may not be too far off from a Druid’s devotion. Plus Druids may fight like Barbarian when their territory is at risk.

Now… looking at the Circle of the Moon, I guess I could force him to join that circle rather than the other one made of mystics and sages.

## Perron’s formula where the integrand of the contour is badly behaved at (and left of) zero

I am attempting to use Perron’s formula to recover the asymptotic form of a summatory function. Namely, it can be shown (is not difficult to prove) that for the prime omega function, $$\omega(n)$$, its Dirichlet series for $$\Re(s) > 1$$ is given by $$D_{\omega}(s) := \sum_{n \geq 1} \frac{\omega(n)}{n^s} = \zeta(s) P(s),$$ where $$P(s) := \sum_{p} p^{-s},\ \Re(s) > 1$$ is the prime zeta function. For example, this relation can be seen by showing that $$\prod_{p\mathrm{\ prime}} \left(1-\frac{u}{1-p^s}\right) = \sum_{n \geq 0} \frac{u^{\omega(n)}}{n^s},$$ and then differentiating with respect to $$u$$. So, in principle, I should have by Perron’s formula that $${\sum_{n \leq x}}^{\prime} \omega(n) = \frac{1}{2\pi\imath} \int_{c-\imath\infty}^{c+\imath\infty} D_{\omega}(s) \frac{x^s}{s} ds,$$ for suitably large, finite $$c > 1$$. But now we arrive at a BIG, nay HUGE, complication, which is that due to the nature of its singularities, it is well-known that $$P(s)$$ cannot be analytically continued at or to the left of zero! I still would like to be able to approximate the contour integral on the right-hand-side of the previous equation.

The next part of this is my attempt to enable this to happen within some not unreasonable added asymptotic error. Please help me to debug my working lemma to accomplish just this.

There are fairly standard bounds on the prime counting function, $$\pi(x)$$, for sufficiently large $$x \geq 17$$: $$\frac{x}{\log x} < \pi(x) < C \cdot \frac{x}{\log x}, C \approx 1.25506.$$ Now additionally, by a Mellin transform, we can write for all $$\Re(s) > 1$$ that $$P(s) = s \int_1^{\infty} \frac{\pi(x)}{x^{s+1}} dx,$$ which is not too bad to evaluate and estimate if we plug in the previous upper and lower bounds for $$\pi(x)$$. Thus my question (I would love to make a little lemma out of this) is the following:

Proposed Lemma: Suppose that $$|R_1(s)| < |P(s)| < |R_2(s)|,$$ for all $$\Re(s) > 1$$, and moreover, the functions $$R_1(s),R_2(s)$$ can both be analytically continued to the entire complex plane, with the exception of at finitely many poles where we consider these functions to be undefined. Then for large enough (but finite) real $$c > \sigma_P$$, do I obtain that the contour integrals are bounded as follows: $$\left\lvert \frac{1}{2\pi\imath} \int_{c-\imath\infty}^{c+\imath\infty} R_1(s) \zeta(s) \frac{x^s}{s} ds\right\rvert < {\sum_{n \leq x}}^{\prime} \omega(n) < \left\lvert \frac{1}{2\pi\imath} \int_{c-\imath\infty}^{c+\imath\infty} R_2(s) \zeta(s) \frac{x^s}{s} ds\right\rvert.$$ Are there any additional necessary conditions that need to be placed on the functions $$R_1(s),R_2(s)$$ to give truth to the previous inequalities?

Thanks in advance. I really do have a good application in mind for this lemma.

## infinite set of mutually irrational numbers which odd linear combinations approximate 0 badly

I’m looking for a set of real numbers $$\{\lambda_i;i\geq 1\}$$ such that for each $$n$$ odd one can control $$\delta_n:=\inf| \sum_i \pm n_i \lambda_i|$$ where the $$n_i$$ are natural integers that sum to $$n$$.

If I don’t want this quantity to be $$0$$ I need the $$\lambda_i$$ to be “linearly independent”, i.e. there should not be integers $$n_1,…,n_p$$ such that $$\sum_i \pm n_i \lambda_i=0$$.

I don’t have a preconceived idea on what should be $$\delta_n$$, I’m not even sure it is possible to have $$\delta_3\neq 0$$.

## How badly should I try to prevent a user from XSSing themselves?

Let’s say a user can store some data in a web app. I’m now only talking about that sort of data the user can THEMSELVES view, not that is intended to be viewed by other users of the webapp. (Or if other users may view this data then it is handled to them in a more secure way.)

How horrible would it be to allow some XSS vulnerability in this data?

Of course, a purist’s answer would clearly be: “No vulnerabilities are allowed”. But honestly – why?

Everything that is allowed is the user XSSing THEMSELVES. What’s the harm here? Other users are protected. And I can’t see a reason why would someone mount an attack against themselves (except if it is a harmless one, in which case – again – no harm is done).

My gut feelings are that the above reasoning will raise some eyebrows… OK, then what am I failing to see?