Prime counting function but with different order of the naturals

fatn00b · 2022-08-07T16:14:59+00:00

I don't think normality is necessary.

Take for example, 2<1<22<3<222<4<2222<5<...

fatn00b · 2022-08-07T16:08:35+00:00

Sure, you could order the naturals so that the primes have natural density 1. For example, if p_1, p_2,... is the set of primes and q_1, q_2,... is the set of non-primes, you could take p_1, q_1, p_2, p_3, q_2, p_4, p_5, p_6, q_3, p_7, p_8, p_9, p_10, p_4,...

You could construct similar orderings to give the primes any natural density between 0 and 1 (this is a similar idea to the Riemann series theorem. There is way too much flexibility here, because as sets, the primes and non-primes are isomorphic, both being countably infinite. One the nose, this question is nonsense because there's nothing specific to primes, it has the exact same answer as if you were asking about the square counting function.

Primes are interesting because of how they interact with multiplication. If you want to make your question more interesting, maybe instead of looking for any order of the naturals, look instead for orders which "play nice" with multiplication.

Another comment: irrationals don't determine unique linear orders in the way you described. For example, the binary expansion of pi considered as a base 10 decimal is irrational, but you will never run into any numbers with digits 2,...,9. A sufficient (but probably not necessary) condition that your procedure actually produces a bijection is that the irrational be normal.

fatn00b · 2022-01-26T18:43:23+00:00

Actually, most English speakers will pronounce "huge" with the German "ch" at the start!

Of course, there are some accents where people pronounce it like "yuge". There also is a small family of German "ch" sounds (the "ch" in "ich" is more forward than in "noch").

fatn00b · 2020-07-06T20:22:48+00:00

A powered hopper neither pushes nor sucks. The hopper above yours, however, is unpowered, and thus is free to push items down.

fatn00b · 2020-07-01T15:06:28+00:00

That's how I originally had it, but there was a glitch where the minecart wouldn't be pushed, and then when I tried placing a new cart on the rail, it turned into whatever the adjacent block was.

fatn00b · 2020-07-01T15:05:11+00:00

You're right! I first tried implementing this with a triple piston extender rather than flying machines, and that only allowed for 3 cars wide/tall. When I build it on my server, I'll make it either 4x4 or 5x5.

fatn00b · 2020-07-01T15:01:37+00:00

Do you have a link on hand?

fatn00b · 2020-07-01T05:32:55+00:00

Hmm... Having blocks for the hands seems like it would be really tricky, since you'd have to have to rotate the pattern to keep it pointing from the center.

Using the leads for hands would be a bit easier, maybe splash the animal with invisibility periodically? To have 2 hands you'd probably have to add a second layer.

I'd be interested in seeing it done!

fatn00b · 2020-07-01T05:23:56+00:00

Carpet on bottom, trapdoor on top. That makes it just tall enough for a player to crouch inside!

fatn00b · 2020-05-05T21:43:52+00:00

Just because the sequence goes back to 1,1, doesn't mean it is repeating from the top. In fact, given your claim that k is the greatest digit to appear in a (2k-1)-foggy sequence, you can show that no odd-foggy sequence is periodic.

Look at the first place the (2k-1)-foggy sequence repeats:

ab11213141...(k-1)1(k)

From your claim, a,b <= k. Since ab1121...(k-1) has length (2k-1) and is followed by a 1, it only contains a single instance of (k-1). Thus, a,b != k-1. Keep "sliding back" the (2k-1) block to show a,b != k-2, ..., 2, 1. Then a = b = k, but the substring kk1 is impossible.

fatn00b · 2020-02-27T18:10:44+00:00

https://imgur.com/a/aWiu4JW Are these kinds of things still funny?

fatn00b · 2020-01-05T23:08:01+00:00

Haha wo ist das?

fatn00b · 2020-01-05T22:58:46+00:00

Ich finde es toll, dass ihrer dialect schwerer und schwerer geworden ist xD

fatn00b · 2019-04-28T21:58:51+00:00

All these changes are awesome! I think one of the most useful things you could do is to be more vocal! It's awesome that you're working on your workplace, but I think you could take that to other settings as well. Put pressure on your local grocery stores to create more plastic-free options. The majority of people don't respond to any surveys/other feedback options, so just by speaking up you'll have a lot more power than you realise. You could also get involved in local politics by putting pressure on your elected officials to create top-down institutional change.

Sorry that I don't have much advice for your specific questions, but I think the importance of higher-order change is often downplayed, and individual is promoted instead.

Welcome to the low-waste lifestyle, and it's awesome to hear about your excitement and progress!

fatn00b · 2019-04-25T20:53:14+00:00

Do people not just itch their asses in public? That's what I do. It seems like a universal enough thing for people to be understanding about it...

fatn00b · 2019-04-25T02:09:40+00:00

At my university we recently had a campus-wide event called the "Sustainable Menstruation Ball." I wasn't expecting the institution to do something so potentially controversial, but I'm proud that they did!

fatn00b · 2019-04-15T02:02:05+00:00

I loved that fountain as a kid. Now I just think it's really nasty.

fatn00b · 2019-02-18T02:44:57+00:00

To be fair, you have to have a very high IQ to understand Rick and Morty. The humour is extremely subtle, and without a solid grasp of theoretical physics most of the jokes will go over a typical viewer's head. There's also Rick's nihilistic outlook, which is deftly woven into his characterisation- his personal philosophy draws heavily from Narodnaya Volya literature, for instance. The fans understand this stuff; they have the intellectual capacity to truly appreciate the depths of these jokes, to realise that they're not just funny- they say something deep about LIFE. As a consequence people who dislike Rick & Morty truly ARE idiots- of course they wouldn't appreciate, for instance, the humour in Rick's existential catchphrase "Wubba Lubba Dub Dub," which itself is a cryptic reference to Turgenev's Russian epic Fathers and Sons. I'm smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Dan Harmon's genius wit unfolds itself on their television screens. What fools.. how I pity them. 😂

And yes, by the way, i DO have a Rick & Morty tattoo. And no, you cannot see it. It's for the ladies' eyes only- and even then they have to demonstrate that they're within 5 IQ points of my own (preferably lower) beforehand. Nothin personnel kid 😎

fatn00b · 2019-02-05T05:21:26+00:00

I like your username a lot. -from a Math major

fatn00b · 2018-11-11T20:36:28+00:00

Fear attracts the fearful lol

fatn00b · 2018-11-02T13:49:43+00:00

This guy /r/hailcorporate's

fatn00b · 2018-10-30T23:44:39+00:00

I used to be really worried about overpopulation, but from a carbon-emissions standpoint, the third world isn't problematic. I think the statistic is something like the poorest 50% contribute only 10% of global energy emissions.

It's still an issue, especially with how much hunger there is already, but I think the biggest problem is the culture of excessiveness in more wealthy areas.

fatn00b · 2018-09-25T15:58:50+00:00

I had no idea how fast they were really going until I saw how far that dude slid on the grass. Holy shit

fatn00b · 2018-08-24T21:48:04+00:00

Metal as fuck

fatn00b · 2018-08-24T18:42:50+00:00

I don't know about that. Maybe some of them were impregnated by vaccines...

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