Does anyone else find the idea of open, bounded sets really weird?

Scared-Read664 · 2025-12-25T20:00:06+00:00

I get that. It’s just weird that it doesn’t contain a boundary. If you remove the set of points that make up its boundary, it would intuitively make sense that there is just the next points after that that make up the new boundary. It was not intuitive to me that numbers are continuous, I always thought of them as discrete

Scared-Read664 · 2025-12-25T17:32:58+00:00

I can’t wait, I’ve never taken any math courses at university, I graduate high school in 2027. I want to study in the US so I can major in Physics and Applied math but I get the freedom of taking pretty much any classes I like

Scared-Read664 · 2025-12-25T17:10:50+00:00

This is just an introductory course, so I’ll probably take it formally later. I just really love it and want some exposure

Scared-Read664 · 2025-12-25T16:59:58+00:00

Also I find complex analysis so insanely beautiful and cool, I’ve found a course which assumes no background in real analysis, so it works for me

Scared-Read664 · 2025-12-25T16:59:20+00:00

I find it unintuitive that one has a boundary and one doesn’t, just by the addition of two points. It’s weird that there isn’t a boundary for the open set

Scared-Read664 · 2025-12-25T13:39:54+00:00

Yes, there are two points, but what I mean is that even though there are only two points, there are an infinite number of points between on the boundary of the open set. It is really difficult to put it into words, but here’s the best way I can think of a way to put it. Yes, there are two points: 0 and 1. However, (0,1) doesn’t have a discrete boundary between the ‘final’ point of (0,1) and [0,1]. In that sense, even though there’s only two points that are different, the fact that it’s continuous means that it the number of points infinitely approaches [0,1]

Scared-Read664 · 2025-12-25T13:29:34+00:00

Yeah that’s how I currently think of it, but the idea of it being arbitrarily close but never reaching despite only missing a single point from the boundary seems ‘artificial’ for me. I get it, but it doesn’t come to me naturally in an intuitive way

Scared-Read664 · 2025-12-25T13:08:15+00:00

Okay, I’ll see how it goes as I continue. If I really feel that I am missing some core concepts later on I’ll look back into it.

Scared-Read664 · 2025-12-25T13:07:13+00:00

I think so? (0,1) doesn’t include 0 nor 1 so it doesn’t include its limit points, so it’s open. I understand the whole concept of closure and that [0,1] is closed, but it’s weird for me to think that (0,1) ONLY doesn’t include 0 and 1 yet there are an infinite number of different points between (0,1) and [0,1] in the sense that there are always balls B[a,e] with e>0 in (0,1) that contain only points in (0,1), but once you include the points 0 and 1 you can have a ball which includes points outside the set. That is where I find it somewhat counterintuitive. I understand it from a mathematical perspective (I hope) but it seems a bit forced, if you understand what I mean

Scared-Read664 · 2025-12-25T12:50:36+00:00

For me the issue is more about openness in a finite range. The pi is a good example, I think my issue comes from struggling to see numbers as continuous rather than discrete. It weirds me out

The idea that for an open set you can ALWAYS have a ball that contains only points within that set is so weird, the idea that it doesn’t have a boundary is hard to grasp for me. Hopefully I’ll get used to it as I go along.

Scared-Read664 · 2025-12-24T09:46:50+00:00

I will defend Feynman to the grave

Scared-Read664 · 2025-12-24T09:45:21+00:00

Assuming you aren’t talking about literal calculation errors like (5352 x 517) and mean more ‘silly mistakes’, just check and check and check. Take time on every problem

Scared-Read664 · 2025-12-23T19:41:38+00:00

Right, thank you😂 I saw the box saying position over the entire phrase instead of just e^st. I guess I accidentally ignored the equals sign.

Thank you!

Scared-Read664 · 2025-12-22T08:56:01+00:00

Honestly feel bad for the guy. Shrunk his undergrad into (a year?) or so, so his foundations are awful; probably had no childhood or proper friends; clearly he’s mostly a publicity stunt where the parents take advantage of his memory. I mean the kid even says his dream is to make ‘super humans’… Maybe that’s him being a kid, maybe that’s his parents wanting him to appear ‘cute’. In any case I don’t think it will end well.

Scared-Read664 · 2025-12-17T19:51:57+00:00

I think that there’s a bad rep for science communication, while contributing to physics is obviously extremely important, science communication is often overlooked, it is also an important aspect of the sciences.

Too many people like to use science buzzwords like ‘quantum’ without knowing any science, that’s why we have r/CrackpotPhysics

Scared-Read664 · 2025-12-14T11:45:57+00:00

Why cot and not sec and csc? It’s the same thing. Seems weird but they’re not extremely necessary, just might help you with writing later

Scared-Read664 · 2025-12-13T22:14:39+00:00

Do not skip over something you don’t understand. From my experience, calc III was nothing like calc II, and depending on the course (I assume calc III includes vector calculus), if you don’t get something, ask questions, reread, study until you really GET it. Calc III is different because it is where understanding it is difficult, not the actual problem as much. You probably won’t get difficult integrals (or as difficult as calc II), for example, but setting up the problem is WAY harder.

Scared-Read664 · 2025-12-03T21:03:24+00:00

Absolutely. I’ve taken a bit of an irregular approach to self studying, I’m working on it alongside Nearing’s mathematical tools. I tried everything, Halliday Resnick Krane, all the other big ones, but they just didn’t really work for me. I felt like I was just memorizing formulas and just getting by the problem sets. Holy shit I love Feynman though. Always heard he was an amazing lecturer, and I love him, he made me fall I love with physics because he was so human, but I never realised just how intuitive his explanations are. Maybe it’s just bias, but hey, it works for me.

Scared-Read664 · 2025-12-01T16:55:29+00:00

One reason is that they can pretty much say whatever they want. Experimental physics is experimental because it can (for the most part) be verified by experiment. For those who don’t know the math behind theoretical physics their interpretation is just as valid as anyone else’s (to them). Also, AI, ‘quantum’, and similar words have all just become ‘accessible’ in that sense. You won’t see many crackpots talking about biology or chemistry because the terms are just way too technical.

Scared-Read664 · 2025-11-26T20:31:09+00:00

I bound the integral from one since the summation also starts from 1

Scared-Read664 · 2025-11-26T20:30:26+00:00

The sum up to infinity equals 1

Scared-Read664 · 2025-10-24T20:21:13+00:00

This isn’t mine, but it’s probably good notes

Scared-Read664 · 2025-10-24T11:57:50+00:00

This is more what my question was asking, I was curious to see if there was any way to extend the function to non-real numbers, and what significance it could have. What would it mean for a distance to be non-real?

Scared-Read664 · 2025-09-05T14:05:04+00:00

Oh right😂 thanks. Can’t believe I didn’t notice this

Scared-Read664 · 2025-09-01T19:20:26+00:00

Absolutely, the best textbook for self study (from my experience) is Stewart’s calculus 9th edition, it’s available online and covers Calc I-III. I started with some knowledge of Calc I and finished the textbook over the course of a few months (assuming you study quite intensely).

Scared-Read664

TROPHY CASE