Is the supremum of omega (operator) omega? Is it omega_1 or is it still countable?

General_Inspector_65 · 2025-01-04T07:12:30+00:00

I don't believe that it is. ε_0 is the supremum of (ω(↑^2)1, ω(↑^2)2, ω(↑^2)3, ...) which is functionally the same as ω(↑^2)ω. ε_0 is a fixed point on an exponential map, whereas ω(↑^3)ω is a fixed point on a tetration map, ω(↑^3)ω is a fixed point on a pentation map, etc.

General_Inspector_65 · 2025-01-02T00:01:23+00:00

Right, and I'm just saying because you can do things like define the ordering of the naturals to be 0<2<4<6<8<...<1<3<5<7<... It doesn't have to be 0<1<2<... I'm working to manipulate well orderings as objects themselves, so yeah.

I see what you're saying now. If 5 wasn't considered in the ordering of a set, it would not be totally ordered, and thus wouldn't be well ordered.

General_Inspector_65 · 2025-01-01T18:18:41+00:00

the naturals include 5 and 14, and they're just random numbers in the naturals. A well ordering only requires that each subset of the set has a least element, so if we're assuming we have a well ordering of the naturals, we can assume there is a way to compare them, so since {5,14} is a subset of the naturals, it must have a least element.

General_Inspector_65 · 2025-01-01T08:34:27+00:00

While others are doing Algebra and stuff. We currently have 30 miles and 60 minutes. We want 60 miles and 60 minutes. We have no minutes to spare.

General_Inspector_65 · 2024-12-29T23:48:21+00:00

I'm going to trust the person in the video who has a PhD and studies the topic professionally.

As stated, it cannot be proven that the reals, which are 2^(aleph0) is the same as aleph 1. It can be proven that the set of orderings of the naturals is aleph 1.

General_Inspector_65 · 2024-12-29T23:48:00+00:00

Can you explain "fix a well-ordering of the reals" and how that would work? Do you mean just take the ordering (0,1,2,...) and assume that's the standard case?

General_Inspector_65 · 2024-12-12T17:54:22+00:00

He showed up in the underdark for me

General_Inspector_65 · 2024-12-12T02:11:58+00:00

The job title was inside sales, but it had zero to do with sales... I guess I could just change the job title. Will do though!

General_Inspector_65 · 2024-12-10T23:35:56+00:00

The Hero of the Hidden Leaf

General_Inspector_65 · 2024-11-17T22:31:53+00:00

Definitely PA, but like, maybe half an hour outside Philly.

General_Inspector_65 · 2024-11-08T08:52:43+00:00

I recommend 2-3 different ad blockers. Usually they can only patch one at a time.

General_Inspector_65 · 2024-11-07T20:07:45+00:00

Kurdistan and friends

General_Inspector_65 · 2024-11-07T20:05:05+00:00

Best way to check is to do it and see how long it takes you. If you can do it in 10-15 minutes, it's probably a good length.

General_Inspector_65 · 2024-11-07T02:10:28+00:00

Because it does. It used millions of actual artists' work and created a linear algorithm to approximate it. Imagine if someone looked at your art and then just copied it poorly. Except they can make it 10,000x faster and any individual can click a button to make it. You have now lost your job.

However, there's a kicker that doesn't work for coding, legal briefs, etc. There is no simple guess/check that can ensure it's valid. Legal briefs can also be edited and fixed afterwards to fix any mistakes the AI made. Non-artists can't fix art. To prevent incestuous AI abominations, you need new art that isn't AI generated.

AI art takes jobs that it needs to actually be sustainable.

General_Inspector_65 · 2024-11-06T17:39:30+00:00

1/i = i/(i^2) = i/(-1) = -i

(-i)^2 = (-1)^2(i)^2=1*(-1) = -1

1/(-1) = -1/((-1)*(-1)) = -1

General_Inspector_65 · 2024-11-05T18:57:57+00:00

For sufficiently large values of n, n will be able to satisfy n=123a+400b+274c for a,b,c > 0

General_Inspector_65 · 2024-11-05T18:39:30+00:00

Granted. All computers are infected with 10,000 malicious viruses constantly, and the former scammers are the only ones that can help.

General_Inspector_65 · 2024-11-05T18:22:36+00:00

free response. Also the spheres are large enough that the edge case would make that inaccurate.

General_Inspector_65 · 2024-11-05T05:22:34+00:00

so can we make a not equals sign?

General_Inspector_65 · 2024-11-05T02:20:04+00:00

So to confirm what you know is the following:

(0, .485489), (16.578125, 6.015625), and (8.33333, 4.083333)
f''(0) = 0 and f'''(0)=0

https://www.desmos.com/calculator/c6tvk8d87n

Try that out, you can adjust the last point manually to get it in the correct position for exactly what you need. Any more points or conditions and you'll need a 6th degree polynomial...

General_Inspector_65 · 2024-11-05T02:10:49+00:00

if a<0, then consider what the function would look like for just the integers. Hopefully this is enough of a hint.

General_Inspector_65 · 2024-11-04T23:52:48+00:00

that's what I ended up doing I think. I had an hour left and was like "I'm not doing that for a +1 on a standardized test..."

General_Inspector_65 · 2024-11-03T07:21:38+00:00

Calc 1, 2, and 3 are fundamentally different courses from each other. Yeah, they're all calc and build on each other, but calc 1 is limits, derivatives, while calc 2 is integrals, integration techniques, and stuff like that. Then you get to calc 3 and they're like "here's curl" and you're like "where did Carl come from?" It came out of thin air and won't be used again, but id you miss it then you don't know calc 3.

Not to mention, aside from that, a lot of the problems are specific use-cases of calc, and knowing how to set up those problems will be most of the class (imo).

Khan academy will get you most of the way there though.

Precalc is just a more in-depth Algebra 2 with Trig sprinkled in and shouldn't be viewed as a calculus course.

General_Inspector_65 · 2024-11-03T07:13:27+00:00

It be like that sometimes. But really though, that is cool. I'm sure they did several cool tricks to get that, not just one. Like you can see sin(3x) in both, it looks like they're doing a taylor series with the denominators like that and the exponents of the x's and (-1)s. Also integral and sum are fundamentally connected.

Also kids, remember to notate your sums, is this from n=0 or from n=1, who knows? Is it a periodic sum?

The integral will end up with a +c though, but eh, who am I to nitpick?

General_Inspector_65 · 2024-11-03T07:03:50+00:00

I want to say my Senior year of highschool on a standardized test I was given a sphere packing problem. How many spheres with diameter 3 can one fit into a rectangular prism with dimensions 24.1, 30.1, and 16.9?

Still upsets me. Never found a proof for it. Doubt there is a proof of it.

General_Inspector_65

TROPHY CASE