chobytes

Various function spaces were definitely brought up in my linear algebra class. That kind of material comes up even in intro differential equations (eg systems of differential equations, Lp spaces).

As I understand it our modern notion of what rigorous mathematics is didn’t exist back then. The justification for analysis was basically physical intuition and simply that it worked.

Euler and company just worked directly with the intuition of infinitesimal quantities. To be fair though, infinitesimals are the essential intuition for how calculus works anyway.

Personally I don’t really care about constructions of the real numbers or technical details of calculus. It’s enough for rigorous mathematics to know that models exist of the theories which produce calculus; that is models of complete ordered fields and even plain old ordered fields with infinitesimals.

Honestly the US gov is playing with fire here. This sort of behavior will only lead to global corporations avoiding doing important business in the US. This is clearly a step in that direction.

I was literally just reading the wiki article before I clicked on HN. Kind of interesting we’re all thinking about this at once.

"requires" is a strong word. the only explicit definition ive seen given for n-ary summations and products products was recursive.

I'm not sure why we thought chalk boards needed replacing. White boards seem generally inferior, and even worse is this newer trend of large computer based boards.

Enjoyed this post. Ive taken linear algebra before, and it does seem obvious that f(v+k)=f(v) just by linearity, but I had never considered the geometric meaning of that before!

Wish I had access to 3B1B when I was just starting to learn this stuff. His expository style and graphics are such great sources of intuition.

Jack demonstrating yet again that he has never used his own website.

Yeah, I'm a student right now and I've come to really like mathematica... I'll probably even get the hobby license after school, but I don't think I could justify the cost of using it professionally.

Yeah he’s like not always nice, but he’s certainly not how I thought. The streams convey a much better personality than his talks or his writing.

Really excited to try the new SQL interface. The old one was less than pleasant to work with.

The Unity stuff is kind of unexpected and I’m curious to try that out too.

...Now I just have to see if my student license lets me upgrade...

ARC only applies to reference types. The programmer has acess to value types, and manual memory management if they want it.

By that measure C++ and Rust are a GCd languages because they have smart pointers.

Im not sure that I think software is always bad just because its old.

I recall working as a technician years ago we used text user interface ticket system from the early 90s. While it wasnt the prettiest system it did its job and one could navigate it quickly once they has commited the keystrokes to muscle memory.

We thought about replacing it with more modern software but after evaluating a few of the options found none of them to be particularly compelling. If anything, we appreciated what our “old” system could do even more.

I had a similar experience working at Macys during the holidays many years ago. I had to listen to about 100 different versions of whatever that “last christmas I gave you my heart” song is every day, and to this day it drives me bonkers when I hear it.

Undergraduate here, and I tend to agree. I used to learn a lot of material online using all the sites, blog posts, videos, visualizations, etc I could find... But as time has gone on Ive realized that most flashy materials, are less helpful that just spending some time with a single good book on a topic.

98/100 in Safari for me.

Just finished my intro linear algebra class yesterday.

The class was a bit more abstract in nature, so some of the chapters in this look like they could be nice application oriented follow ups to it!

Doctors do a really poor job explaining to patients just how hard it can be to get off of some of these drugs.

Personally it took me over a year to taper off of venlafaxine due to intense discontinuation.

While youre on it at full dose, forgetting to take it even one day is a miserable experience.

With Robinson’s hyperreal numbers(1), I see no reason not to just freely use infinitesimals again.

(1)https://en.m.wikipedia.org/wiki/Hyperreal_number

The hyperreals make the concept of infinitesimals rigorous as well, while preserving intuitive ease.

eg Something like 'limit(f(x),x->a) = L' is just 'f(x) ≈ L when x ≈ a'

i didnt realize leses had so much history and theory behind them!

Exciting news. My only hope is they they would simultaneously dial back medication advertisements.

This. I'm legitimately scared when random guys approach me, as I've had guys grope me, try to corner me, etc in past. Sadly, I feel like these are common experiences for women.

They're treating people as objects to be measured and quantified. The sentiment analysis thing at the end sounds borderline sociopathic.

I would personally be terrified of anyone who thought this was an ethical or acceptable thing to do.

Serverless has gone too far

This sounds like a giant red flag to me.

I hope you at least disclose your methods to people you contact.

are you sure none of them are boys? :^)

i genuinely cant tell if satire. A+