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How do Alternate Natural Attacks work with a Shifter/Kraken Caller Druid?

So I’m working on building Doctor Octopus and looking to add tentacle attacks (without using a cheesy synthesist summoner). A Kraken Caller Druid gets two at 4th level in their natural form (and more later). I was thinking about adding a 1 level dip in Shifter and make use of their Alternate Natural Attacks to turn their two claw attacks into two tentacle attacks, but I’m unsure if I can.

Here is the Alternate Natural Attacks text:

A shifter can draw on her chosen animal aspect to transform her hands into deadly weapons, as represented by the shifter’s claws class feature, but not every animal has prominent claws. The following list provides alternate natural attacks for the shifter claws class feature. Each time the shifter activates her shifter’s claws ability in her natural form, she can manifest one of the alternate natural attacks listed below for any of her chosen aspects, or those that relate to her archetype. Each alternate natural attack replaces one of the shifter’s claw attacks. The shifter can gain up to two different alternate natural attacks with this method. These alternate natural attacks modify only the damage type of the shifter’s natural attacks and otherwise function exactly as the shifter claws class feature.

The bolded part is the part that’s tripping me up. I, of course, want to go with an Octopus aspect, which has these natural attacks listed:

Octopus: Bite (B, P, S), tentacle (B).

Am I able to turn my two claw attacks into two tentacle attacks? Or would I have to turn one claw into a bite and one into a tentacle?

Also, if I turn one or more claw attacks into tentacles, do my whole arms become tentacles thereby making them unusable for other things?

And can I take Alternate Natural Attacks with the Adaptive Shifter archetype?

Finally, am I correct that when using the Kraken Caller’s Wild Shape ability to add tentacles while in my natural form I can also stack on Shifter’s claws?

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Inconsistent natural scroll wiht synaptics on Kubuntu 18.04

Dell Latitude 7470 Like the distro, especially HiDpi handling, but it’s very disappointing that natural scroll mode is inconsistent. Freshly installed Kubuntu 18.04 came with libinput, but I just went and simply installed xserver-xorg-input-synaptics-hwe-18.04, after which a lot of settings unlocked in system settings -> input devices -> touchpad. Works great besides the fact that in many native KDE interfaces (app launcher scroll, some widgets scroll, selectbox scroll) it does not work in “natural mode” which is confusing to say the least, although in settings it is enabled and works as expected in apps other than most of native kubuntu apps.

Any idea on why Youtube videos don’t follow the natural reading direction with the title? [on hold]

I’m writing an assay on designing the layout, and while researching the diagonal layout design pattern (setting the elements to align to left on the top, and to the right on the bottom to properly follow the users reading direction), and while doing it I’ve noticed that the Youtube player only follows the rule to some extend, and you can see in pretty much any player view:

enter image description here

As you can see, the player has the title in a quite hard to see spot, while maintaining the correct position of the feedback buttons and the subscribe button. Usually, as is shown in online articles, the header is always placed above the content and aligned to the left for the mentioned reading direction.

I was wondering why would Youtube go for this approach. The first thing coming to my head is that simply youtube thinks you don’t really need the title all that much since most likely you clicked on it to get to the video, but I don’t like jumping to conclusions.

Haven’t been able to find any good research on the topic, therefore I’m asking here.

Sorry if this is a rather noob question. I am still a beginner to be honest. Any help would be amazing 🙂

Is the language { | p and n are natural numbers and there’s no prime number in [p,p+n]} belongs to NP class?

I was wondering if the following language belongs to NP class and if its complimentary belongs to NP class:

\begin{align} C=\left\{\langle p,n\rangle\mid\right.&\ \left. p \text{ and $ n$ are natural numbers}\right.\ &\left.\text{ and there’s no prime number in the range}\left[p,p+n\right]\right\} \end{align}

I am not sure, but here’s what I think: for each word $ \langle p,n\rangle \in C$ we know that the word belongs to C because there exists a primal certificate – an nontrivial divisor to any of the numbers between $ [p,p+n]$ , though I am not really sure it is in NP.

regarding the complement: I think it is in NP because the compliment compositeness can be decided by guessing a factor nondeterministically. But again I am not so sure about it and I don’t know how to correctly prove and show it.

Would really appreciate your input on that as I am quite unsure and also checked textbooks and internet (and this site) about it.

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Peano axioms: prove that there is no natural number between n and sucessor of n

Let $ m \in \mathbb{N}$ . Show that $ \nexists n \in \mathbb{N}$ such that $ m < n < s(m)$ , where $ s$ is the successor function.

Here’s my proof using only the Peano Axioms I was introduced. I’d appreciate someone to check my work.

Let’s prove it by contradiction. Suppose that $ \exists n \in \mathbb{N}$ such that (1) $ m < n$ and (2) $ n < s(m)$ .

From the definition of order we have that:

(1) implies that $ \exists c \in \mathbb{N} \setminus \{0\}$ such that $ m + c = n$ .

(2) imples that $ \exists c’ \in \mathbb{N} \setminus \{0\}$ such that $ n + c’ = s(m)$ .

Therefore $ $ \begin{align*} n + c’ + c &= s(m) + c\ &= s(m + c)\ &= s(n)\ \end{align*} $ $

Since $ c’ \neq 0$ and $ c \neq 0$ , we know that $ c’ + c \neq 0$ and therefore $ \exists k \in \mathbb{N}$ such that $ s(k) = c’ + c$ . Hence:

$ $ \begin{align*} n + s(k) &= s(n)\ s(n + k) &= s(n) \rightarrow n + k = n \rightarrow k = 0 \end{align*} $ $

Since we’ve concluded that $ k=0$ , we have that $ s(k) = s(0) = 1 = c + c’$ , where follows that $ c$ or $ c’$ needs to be equals to $ 0$ , and that is a contradiction.

I also have one more question… After defining what a function is, can’t we conclude that $ s : \mathbb{N} \setminus \{0\} \rightarrow \mathbb{N}$ is actually $ s(n) = n + 1$ ?

If so, using that the proof would’ve been more immediate…

Any kind of comments and critics are highly appreciated! Thank you!