Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
1 to 24 of 24
where does one find references to the symbolism used in the set theory?
We could easily create $n$Lab pages, where missing, that explain whichever symbol needs explaining.
You mention:
A≠B⇔∃x((x∈A∧x∉B)∨(x∈B∧x∉A)
Which of these symbols are unclear? All? Some? Let’s start with one of them.
Maybe start with https://en.m.wikipedia.org/wiki/Set_theory#Basic_concepts_and_notation and/or perhaps check out some books on elementary set theory. The website mathematics.stackexchange is a great place to ask focussed questions on specific mathematical concepts or problems you may encounter. I strongly suggest browsing the site to see what style is the norm there, and what leads to fruitful answers. All the best.
David, why that urge to move discussion away from the $n$Lab, here and elsewhere?
I have started logic symbols – table. People should be invited to expand on it.
It’s makes for quite an exercise to see what it would take to understand Chip’s A≠B⇔∃x((x∈A∧x∉B)∨(x∈B∧x∉A) solely through nLab pages.
He needs at least to know that material set theory is generally presented as a first-order theory with a binary relation ∈, hence the mix of logic and set symbols (#3), and that this theory expresses set identity through extension.
How would you find this out? If by chance you reached material set theory, until 5 minutes ago you wouldn’t have had a link to the axiom of extensionality. Now you do, you find that ∈ is an extensional relation. So now ∈ is to be compared to $\prec$ at the latter page. But how many beginners will see that the ’set’ on which $\prec$ is a relation is a set of sets for ∈?
Let’s not make it more complicated than it is. He was asking for the meaning of the basic symbols.
Sometimes it is good to remember that there are people out there who have yet learn everything from scratch. We can easily provide a little guidance, long before it gets to subtleties as the distinction between material and structural set theory.
I just talked to a lot of students at Nesin Math Village in Turkey. There, Wikipedia is blocked, and I learned that the nLab is a common source of information. This is young human beings who want to get basic information. And it’s not hard to provide, I just did it: logic symbols – table.
Of course, I share your wish that people have access to basic information, and it’s great to give whatever we can. Better to have that table than not have that table.
My point was rather to think about how difficult it would be to find one’s way about the nLab if you wanted to understand the meaning of A≠B⇔∃x((x∈A∧x∉B)∨(x∈B∧x∉A) and were surprised to find set theoretic and logical notation combined. Perhaps Chip could tell us whether the logic symbols – table suffices. I’ve just added in ∉.
Actually, things are even trickier. Looking back, Chip (#1) was struggling with the page inhabited set. Imagine you were present watching a student who had somehow navigated to this page. Wouldn’t you want to warn them that there are subtle issues regarding constructive thinking going on there that could be left to another day?
I just talked to a lot of students at Nesin Math Village in Turkey. There, Wikipedia is blocked, and I learned that the nLab is a common source of information.
Wow. That’s just… wow. Maybe I’ll mention that in the Broader Impacts section of my grant proposal. (What level were these students? College? High school? What pages were they looking at?)
I agree that it’s great to add basic information if we are able to spend the time. I think David R’s point is that here at the nLab/nForum there are a very limited number of people, and our primary focus is not on helping people with very basic questions, whereas MSE (for instance) has a huge number of people and is explicitly for the purpose of helping people with even very basic questions. So someone with very basic questions may be better served by asking them at MSE rather than here.
Did they mention whether stackexchange is also blocked at Nesin? What about the arxiv?
Hi Mike,
the participants in our workshop were master students and PhD students. They told me that they use the $n$Lab regularly, but find it often frustrating that the entries are too advanced. I think if we could, slowly but surely, have more textbook-style basic material, it could eventually have a big impact.
It is only Wikipedia that is blocked in Turkey. Sites such as MathOverflow and the arXiv (and the $n$Lab) work just fine. I heard that the situation in China is similar, and presumably for similar reasons: There is no politics on the $n$Lab.
The main business of Nesin Math Village is to prepare highschool students for their final exam. At any time, there is a swarm of them around. My understanding is that tuition fees of these students is what keeps the site running. But cross-financed by that, there is advanced and research activity for a select few. It feels a bit like a combination of Oberwolfach and a mediterranean vacation resort. The scenery is dramatic, the housing is rustic (for advisors, that is, the students sleep in tents), all buildings are completely in natural stone. The bread is baked on-site in a wood fire oven.
It felt at times too good to be true that such a place can exist. I have to admit that I didn’t know about it before I went there. But I learned that in Turkey the Math Village is famous and its founder, Ali Nesin, is a national celebrity, as was his father. There are regularly tourists passing through the Village. It happened that I was looking up from my computer while in the commons area, only to see that some family was taking pictures of us working.
When wondering about this, it was highlighted to me that it is not for nothing that Turkey is one of the few (the only?) country on Earth that has, with Arf, a contemporary mathematician portrayed on their banknotes. There used to be Gauss and his bell curve portrayed on the 5 Deutsche Mark note before the Euro was introduced, but that seems no match to having the expression for the Arf-invariant on the 10 Lira bill!
My lecturer colleague Murad Özaydin, who did his B.S. with Arf, joked, after paying for dinner: "I just gave them a piece of paper with the picture of my advisor, and they were happy."
Thanks for the information! I definitely support the gradual inclusion of more textbook-style basic material.
How ’basic’?
How ’basic’?
Usual math style. Introduce the concepts before using them.
I’m still thinking about someone quite early in their education reaching HomePage and the next steps they might take. We don’t really say in the ’Purpose’ section that some pages are expositions of introductory material. Since we have a collection of more introductory articles, how do people feel about a link from there to a page which lists designated introductory material?
It may not always be possible to separate out the introductory material, but we could point to pages which are pointedly such. In particular these are Urs’s pages of his courses
Introduction to Topology, Introduction to Stable homotopy theory, Introduction to Cobordism and Complex Oriented Cohomology, Introduction to Spectral Sequences, …
and other pages
Logic isn’t so well served, contrast homotopy type theory FAQ with string theory FAQ. logic and type theory could be included. We could do with someone teaching an nLab-based course on these areas.
I agree our pages on logic could use some love.
I certainly think that idea if a list of introductory material would be useful. I did start some pages on modal logic, but (i) they probably were not introductory enough, and (ii) the importance of the general area has exploded so that the introductory aim of those pages has been superceded to some extent.
Chip, what browser and OS are you using?
I might get just as deeply or circularly lost as I did just reading ’homotopy type theory FAQ’.
That page is left in skeletal state and not meant for public consumption. Maybe it should be deleted.
I had started writing this, ever optimistically. But I gave up after we got bogged down in discussions of some basic point right away.
Chip, regarding “musings” as in the last part of your #18 and similar musings in previous messages of yours: This is not the kind of exchange suitable for this forum. You should stick/get back to actual maths questions, if you have any.
You had initially asked for the meaning of various logical symbols, and we had given you a first pointer here. I doubt that the entries linked to there are expository enough to actually serve as decent explanation of these symbols. So you should ask a followup question and thus make somebody improve the respective entries!
1 to 24 of 24