No, turtles never even existed, I’ve never seen one. /s
Anarchist, autistic, engineer, and Certified Professional Life-Regretter. I mosty comment bricks of text with footnotes, so don’t be alarmed if you get one.
You posted something really worrying, are you okay?
No, but I’m not at risk of self-harm. I’m just waiting on the good times now.
Alt account of PM_ME_VINTAGE_30S@lemmy.sdf.org. Also if you’re reading this, it means that you can totally get around the limitations for display names and bio length by editing the JSON of your exported profile directly. Lol.
No, turtles never even existed, I’ve never seen one. /s
Infinite-dimensional vector spaces also show up in another context: functional analysis.
From an engineering perspective, functional analysis is the main mathematical framework behind (1) and (2) in my previous comment. Although they didn’t teach functional analysis for real in any of my coursework, I kinda picked up that it was going to be an important topic for what I want to do when I kept seeing textbooks for it cited in PDE and “signals and systems” books. I’ve been learning it on my own since I finished Calc III like four years ago.
Such an incredibly interesting and deep topic IMO.
I actually designed a digital equalizer using an IIR filter this semester, which actually does theoretically work on sequences of numbers, which constitutes an infinite dimensional vector space. The actual math was just algebra and programming, but it was an implementation of a Z-transform transfer function which is a sequence operator (maps input sequence to output sequence).
IMO infinite-dimensional stuff shows up in two types of problems:
For some reason, you need to solve the partial differential equation you started with, i.e. you can’t use symmetry or approximations to simplify it into an ordinary differential equation.
When you’re dealing with signals that change in time or space, you have to decompose those signals into simpler signals that are easier to analyze.
some wysiwyg editor for LaTeX
LyX is basically that.
IMO LyX is way simpler than LaTeX for basic stuff, but because it is literally not Microsoft Word I couldn’t really use it to collaborate with people this semester, let alone convince them to work on a full LaTeX document. LyX would be the way to go if my colleagues were even remotely interested in learning about literally anything. You can lead a horse to water, but you can’t make it drink…
Yes.
Would be great for me and others who have trouble with body language. I could deepfake a version of myself with neurotypical body language and offload the effort of “acting normal” to the AI for interviews and video calls. Genuinely I’m super pumped for this.
Welp my brain is sufficiently melted. 10/10.
In all seriousness, this is really cool!
@Mistral@lemmings.world That’s great! Can you rewrite the proof so a dog can understand it?
Also I’ve seen a few proofs of the FTC at various levels, but I’ve never seen a proof by contradiction be used. It can be done by plugging in definitions and properties of the integral into a milquetoast delta-epsilon proof. It’s less than a page for both theorems in “baby Rudin.” The hard part IMO is building up all the results you use, but once you have them it’s an easy proof.
It’s screwed up a couple times. For example, the bit about “by the properties of limits you can interchange the limits” is hilariously untrue.
@Mistral@lemmings.world Okay. Now can you rewrite the proof in language a five-year-old would understand?
For anyone else reading this [1], a partition of an interval [a,b] is a finite set of points satisfying the condition a = x_0 ≤ x_1 ≤ … ≤ x_n-1 ≤ x_n = b. So the max(P) = b, so the condition max(P) -> 0 just means b -> 0, which is wrong.
[1] But like, y tho?
@Mistral@lemmings.world In the previous output, I think that you mean “max(norm(P))” where you say max(P), right? The condition “max(P) -> 0” just smooshes the partitions into the origin.
@Mistral@lemmings.world I think the proof of the second part was fine; it was the first part where the interchange of limits was used and was therefore erroneous.
@Mistral@lemmings.world Please continue.
Why I do this to myself lmao
@Mistral@lemmings.world You said “By the properties of limits, we can interchange the order of the limits”, but you can’t in general interchange the order of limits except under strict circumstances.
@Mistral@lemmings.world Please continue.
If that happens then I swear to fucking God I’m done with YouTube forever.
Edit: i.e. if it breaks FreeTube, Invidious, Sponsorblock, etc. (because I’m already done with the main site forever) then I’m out. If the choice is between content vs no ads, I’ll take no ads even if it means no content.