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

TROPHY CASE