stackdynamic

Recently I have been interested in the Calculus of Constructions and read the Wikipedia Page. Now, the content on this page is all well and good, but I have also been reading the lean theorem proving manual and have some confusion. I understand the broad idea of how CoC can be used to prove things: for example, in the below Lean code:

theorem t1 : ∀ (p q : Prop), p → q → p :=
λ (p q : Prop) (hp : p) (hq : q), hp

We have a proof that for propositions p, q , p → q → p by treating the proposition as a type, and constructing a term of the correct type. This is the Cur

I know that the number of available testing centers decreased a lot after fall break, but now that students are returning, are old locations going to re-open? Having one right in ISR fall semester was so nice :(.

I am currently in a double in ISR without a roommate, and would like to know if I have been assigned one. I can't see anything on the housing portal. Would anyone happen to know?

I am a freshman planning to take 225 next semester. I see 296 up on course explorer, but the description doesn't actually state what topic 296-25 is doing this semester. Would anyone happen to know?

I am a freshman living in a dorm double right now, and my original roommate had cancelled their contract for the year, meaning I effectively am in a single, which is quite nice. Does anyone know if students currently without roommates will be potentially assigned ones for spring semester?

I've been working through a few texts lately and have noticed that I seem to retain information better when I am using a physical version rather than a PDF. I am curious as to what everyone else prefers. I like PDFs for the following reasons:

• clickable links
• easy to copy figures into my notes when I do them in LaTeX
• searchable text
• often cheaper or free

Pros of physical textbooks:

• research shows physical textbooks have better information retention
• doesn't involve staring at a screen for long periods of time
• can annotate and write in margins easily

Also curious about preferences regarding hardcover vs paperback.

For incoming freshman: you can see what you have credit for through self service (registration & records > student records and transcripts > view academic history). Just became available a few hours ago I think. You can reverse engineer your score using this page: https://admissions.illinois.edu/Apply/Freshman/college-credit-AP.

A neat bit of syntactical sugar is that for loops can have else clauses which run if no break statements were encountered. This means that something like:

for i in iterable:
    if i == 2:
        print(":)")
        break
else:
    print(":(")

Is all well and good. However, I am curious as to why there is no optional elifs, as this seems generically useful. This for example:

for i in iterable:
    if i == 2:
        print(":)")
        break
elif iterable == [1, 7]:
    print(":|")
else:
    print(":(")

Gives a syntax error. You could of course nest further if statements in the else clause, however this isn't always the prettiest.

Hello there, I am currently a HS student with a fair amount of programming experience. I would say I am fairly versed in general CS principles, with good knowledge of various data structs and algorithms, OOP, DP, etc. The two languages I currently primarily program in are Python and C#, both of which I feel fairly comfortable with. Now, recently, I signed up for the AP CS test, which uses Java. Looking at past problems, I feel confident I could solve all of them fairly easily with Python, however, I don't really know any Java. I do know that C# and Java are relatively similar languages, which is why I feel good about being able to pick it up fast--again, on the general CS/problem solving sid

I'm looking for an approximation of a battery discharge curve over time, which looks like this. In essence, it is the "reverse" of a boltzman-sigmoid, which plateaus, decreases and then plateaus, decreasing, plateauing and then decreasing. Assuming it is some combination of exponential functions, would anyone have any ideas?

I stumbled across this when messing with series that converge to Pi. The fact that $4\sum_{n=1}^x\frac{x}{x^2+n^2}$ converges to Pi as x approaches infinity follows from evaluating the integral on the right side of the below equation via a Riemann Sum and then simplifying:

$$\frac{\pi}{4} = \int_{0}^{1} \left(\frac{1}{1+x^2}\right)\mathrm dx$$

I noticed that the convergence rate seems to have a lower bound (not sure if that is the correct use of the term) of 1/x, but my attempts at a proof for this haven't really gone anywhere (made a feeble attempt at induction, which looked promising at first, but quickly got stuck). I am currently a HS student so I have a limited unders

Hi, apologies for the probably obvious question, but I'm getting compilation errors when using the reflection probe node in shadergraph (version 3.0.0 on HDRP).

Here are the relevant parts of my graph as shown below:

https://i.redd.it/nuq2gm12w4m11.png

As you can see, I supplied the necessary inputs (view direction, normals and LOD) and am outputting directly to emission in my master node. I have my reflection probe component attached to the child of the plane using this shader, set to real time (I doubt this matters, adding for comprehensiveness). Anyways, I'm getting these errors when I save my shadergraph:

![img](6aym79h4w4m11 " Could someone tell me what I might be doing wrong