Rushabh Mehta

@Angel, you know better than to flood the comment section. Create a chat room and please move all of the messages there.

Never mind, seems like it's been figured out

Just got E-pic on DBA, if anyone wants to dig through my history

Ah the penny hats are all suggested edit based, no wonder I haven't gotten them

Hmm I'll give it a shopt

@MadPhysicist I don't see it...

@RoryAlsop Definitely not. Otherwise you'd think there'd be a lot more of it.

Just got Satellite View. Any clues as to the trigger for it?

@double-beep I think so, since I got it as soon as I upvoted an answer on my question

What is console? I've seen a lot of people talk about it here. Is it a way to query the site?

Ah, on two sites @Wolgwang

I got my 3 secrets 3 hours ago

When will I be getting detective hat, by the way?

I did do some close votes on Math.SE

@JoeKerr No

Dunno. Will keep hat hunting for now!

It is interesting, since I'm not sure whether the upvoting, the new account, or the first question was the trigger for these hats (maybe each for a different hat?)

Is there any info on what the triggers for these hats are?

Monologue, Dialogue, and Spotting scope

I just received 3 secret hats after joining a new stack site and asking a +1 question

@dxiv Fair: I retract my previous claim. Although I'd argue that the fallacy is before that. It is the step of having a countably infinite sequence of reals, and then choosing another.

@CalebBriggs Great summary!

@dxiv You can do that, because there is a consistent rule you apply, meaning that you don't run into choice-like considerations.

@CalebBriggs You haven't defined any limiting case at all. You haven't described how to extend this process to infinite sequences of reals. Only finite. Similar to the example in my second comment.

@dxiv You can't even do it countably many times, forget uncountably many.

@CalebBriggs See my second comment.

Here's a simple example to show the flaw in your thinking. I can add one to $0$ as many times as I want, and still get a natural number. Does that mean I can add infinitely many ones to $0$ and get a natural number?

@MarkSaving OP means that there doesn't exist a strict least upper bound for any number (i.e., a number greater than the chosen number, but there aren't any numbers in between)

What's the justification for being able to do this $2^{2^{|\mathbb N|}}$ times? Just because you can do something any large number of times doesn't mean you can do it infinitely many times.

@TedShifrin What rules are you referring to?

@XanderHenderson You know the rules of hyperfunctions and so do I

Yes, this is what the main site is for, Rithaniel.

@Rithaniel It isn't like you can't ever ask questions here, but for questions that are askable on the main site, they shouldn't be asked here.

This isn't really the right place to ask this, we have a Q/A site for a reason

@XanderHenderson Why do you choose to be this way.

@anakhro And yea! That was part of my plan for the lecture. It's around 20 students, so it should be fun. But I need to write up course notes for students with disabilities and others who want to prestudy, but I finding it a lot more difficult for the reasons I mentioned.

@TedShifrin Makes me feel good about my bad grades in uni. Loved the subjects, but still always did bad :(

@anakhro Sorry, I'm back. Planning to cover up to Lowenheim Skolem and Henkin Models. It's a long course.

Do you think handwaving over the axioms with a intuitive understanding of what logical formulas are to begin the study of set theory, followed by propositional logic and later first order logic makes sense? Or is there a better way to order and present things? I just don't know.

I'm currently writing up some course notes for a course I am teaching on first order logic and the basic theorems. I'm struggling with where to start, however. I want to start with sets, but I'm tempted to do a breakdown on why each axiom in ZFC is important (and give the axiom of regularity some love), but in doing so, there needs to be some level of understanding of definable relations/logical formulas/set maps, which requires first order logic.

Simple!

dx just means, the variable we are integrating on is x.

is viewing it as notation only

But for now, I think the best way to think about it

Point is, dx is defined differently depending on which subject you learn it as part of

Ah well, seems like you left

If it's right, no issue with me. If not, I'd like to put you on the right path.

I'm not arguing! I'm enjoying this. I'm just trying to understand what your perception of dx is.

@Tim dx is not a function. Neither is dy/dx (unless you mean that it is a function on the space of functions, to which the answer is, kinda)

"𝑑 makes x both infinitesimally small and work with functions at the same time." What does this mean? dx doesn't work on a function, either. (Not trying to call you out here, but it's important to clear out misconceptions.)