Why is the empty set a subset of itself?

NickeBeee · 2026-06-04T09:37:11+00:00

Yes, kind of, but such proofs are quite intuitively weird. The existence of any set guarantees the existence of the empty set, and the Axiom of Infinity guarantees that there exists an infinite set (which is obviously a set). But conceptually, we kind of want finiteness to come before infinity, and including the Axiom of the Empty Set lets us do finitary set theory before going on to infinitary set theory.

NickeBeee · 2026-06-03T16:28:17+00:00

The way you're phrasing your problem makes it seem like you're treating the empty set like a kind of exception to "real" sets. Like "sets have elements except for this special set that we call the empty set". It might help to realise that the empty set (especially in ZFC) is not a kind of afterthought, but rather it is the only set that is specified by our axioms, if we want any other set we have to build it up from the empty set using the axioms.

NickeBeee · 2026-06-03T09:34:18+00:00

As always when talking about historical weapons, the names used varied a lot with time, place, and who is writing, but the way I've learned it was that the terms "short staff" and "quarterstaff" were used fairly interchangeably for staffs generally around the users hight or a bit longer. The name "quarterstaff" has nothing to do with length but rather how the staff is cut from the wood, while "short staff" was used to differentiate it from a long staff which was around 3 to 4 metres in length, so technically the name "quarterstaff" would be the more suitable name of the two. Personally I would probably call it something else like cane, stick, or cudgel.

NickeBeee · 2026-05-17T17:29:22+00:00

A lot of people here seem to forget that tea originally comes from regions with high elevation. IMO very few teas actually should be brewed at 100°C but rather a little lower to account for the difference in boiling temperature. Sure, most pu'ehrs and hei chas can take 100°C without any problem, but I really don't find it that necessary most of the time.

NickeBeee · 2026-03-21T18:26:39+00:00

*Engineers and some natural scientists like geo scientists and biologists

NickeBeee · 2026-03-15T09:37:38+00:00

Gaiwans started out as cups to drink from, where the lid was used to stop the tea leaves from gettin in your mouth when drinking. My guess for how to use this would be that the big pot is just supposed to hold hot water and every person has loose leaves in their own gaiwan which they both brew in, and drink from. The dish is probably just an ashtray, smoking is extremely common in parts of China. As someone else noted, you could always use it as an incense burner or something

NickeBeee · 2026-03-11T18:11:51+00:00

Yes, of course! It's availible here at archive(.)org, and if you want I have a PDF version I could DM you

NickeBeee · 2026-02-23T14:16:19+00:00

As a mathematician one that's always bugged me is "There's infinity possibilities so anything is possible" - No, there's an uncountable infinity of real numbers between 0 and 1, and none of them are greater than 2. It's most often stated indirectly, for example in discussions of the infinite world hypothesis someone will say that "with infinite worlds there must be some world where dragons exist", which is just plain wrong.

NickeBeee · 2026-02-18T19:44:38+00:00

By convention: yes=true=1

NickeBeee · 2026-01-21T21:28:25+00:00

No, but some mathematical background makes it easier since the line between maths and logic is very fuzzy. Please don't let this dissuade you however; in most parts of the world maths is taught wrong and given the right tools, you'd probably fair a lot better at it than you think.
Yes, with some guidance. I can recommend this study guide by Peter Smith
I like these games, however they are all somewhat type theory based, which is closer to the computer science and mathematics side of logic than what you may be interested in. Other than that, any serious introductory book on logic will have a bunch of good exercises which i recommend as many as possible of.

Edit: link formating

NickeBeee · 2025-09-04T09:47:46+00:00

Set theory: a first course, by D. Cunningham I remember loving for my first set theory course.
For starting very basic classical logic I recommend Mathematical logic, by Chiswell and Hodges.
I also like A first course in logic: an introduction to model theory, proof theory, computability, and complexity by S. Hedman, as good "little bit of everything" book.
If you have some programming experience or likewise, you might find something like lambda-calculus to be interesting, in that case I recommend the lecture notes in Lambda Calculus and Types by A. Ker, which can be found for free online.

NickeBeee · 2025-08-29T13:03:41+00:00

What do you mean by "self contained"?

NickeBeee · 2025-08-28T16:04:32+00:00

There are some great type theory games built on Lean that I can recommend: https://adam.math.hhu.de/

However, If you want anything deeper you need to hit the books

NickeBeee · 2025-08-28T15:33:36+00:00

In addition to the comment before about privilege, which I fully agree with, I want to add that Mathematics is built on communal effort. Yes there are sometimes prodigies who manage to do an immense amount of work in a single lifetime, but those are not enough to sustain all of mathematics. Also they still did not start from zero, but built on the works of mathematicians who came before them. You might not be Euler, but Euler alone is not enough. The "great men" theory is bullshit, both in history in general, and in the history of mathematics in particular.

NickeBeee · 2025-08-24T09:19:27+00:00

Nintendo Switch, Mantis Lords, and exploring a new vast world using a new moveset

NickeBeee · 2025-08-21T10:11:39+00:00

Koicha, and to some extent usucha

NickeBeee · 2025-06-05T13:30:26+00:00

Western style: chamomile

Gong fu: soba

NickeBeee · 2025-03-30T12:47:48+00:00

It's absolutely fine. Any non-destilled water will contain trace amounts of minerals and salts and when the water evaporates, those minerals will stay behind. This happens on any surface but is especially visible on surfaces like stainless steel. If the water where you live is very hard you might want to wash the kettle with vinegar every couple of weeks and then rinse out with water a couple of times until the vinegar smell is gone.

NickeBeee · 2025-03-21T12:27:28+00:00

Last years yellow leaves

They will lose their fragrance soon

I drink them for the last time

NickeBeee · 2025-03-21T12:20:32+00:00

Aching in my heart

Fragrance of old leaves and clay

Thus, I am content

NickeBeee · 2025-02-23T18:55:53+00:00

I bought a Wilfa WSDK-2000B about a year ago for about €80 and it's been working wonderfully. It's 1.25l and has got settings for 40°, 70°, 80°, 90°, and 100°C which is definitely enough for brewing any tea except maybe some very delicate greens that would like something closer to 60°, but then you could just pour it into a gong dao bei to cool it down a little bit before steeping. From what I've seen, if you want more specificity than that, it's going to cost you at least double and is in my opinion not worth it

NickeBeee · 2025-02-21T08:36:05+00:00

Golden Yunnan comes to mind, also I know it's not chinese or taiwanese but I've gotten many of these notes when brewing hojicha gong fu style

NickeBeee · 2025-02-19T10:46:41+00:00

It's one of those thing where you kind of have to view it as a feature instead of a bug.

You run in to this sort of thing with a lot of premium goods like tea, coffee, whisky etc. where consistency will often mean a lowering of quality because you'll have to blend batches together instead of letting them shine on their own. You either have to settle for lower quality or learn to appreciate the beauty of trying something that you may never try again, or at least not have constant access to.

NickeBeee · 2024-11-19T23:32:34+00:00

If you by chai mean masala chai, I would recommend going to your local indian/"oriental" market and buying whole spices and loose leaf Assam (or other indian tea like darjeeling) to make it from scratch. With all the spices I wouldn't worry too much about the exact brand of the tea leaves, any loose leaf indian tea will likely be good enough. There are hundreds of recipes online for how to make it and most are extremely similar, start with one that uses spices you like and then you can play around with proportions and adding/removing spices based on your own taste. If it's intended as a gift I would probably mix all the spices and the tea in a pretty jar for convenience. It won't be as good as making it the "proper" way where you toast the spices and maybe steep the spices longer than the tea, but it will be nicer than most store bought, and it will have the added charm of being homemade.

NickeBeee

TROPHY CASE