12:24 AM
-8

This is based on a number of questions, relating to people using "urgent" in the title (homework due the next day), general trends in questions becoming easier (more people using this site as a quick way to get homework done). On Physics there is a dedicated tag to homework, which has guidelines...

1 hour later…
1:40 AM
@MartinSleziak I went ahead and created tag. We will see what other users think about this and whether it will remain as a separate tag or we will have synonym between this tag and (in one direction or the other).
2

There are many questions about well-ordered sets on the main and I consider well-orders to be an important topic. So perhaps they could deserve their own tag. On the other hand, many questions about well-orders are at the same time questions about ordinals so tagging them by both ordinals and (w...

I will also add link to the tag-excerpt and tag-wiki for ordinals.
BTW the question for people who speak English better than me - in this sentence: "operate as a direct extension of the positive integers for transfinite inductions." Is there some reason for saying transfinite inductions rather than transfinite induction?
I have also created very basic tag-excerpt and tag-wiki for well-order.
If the consensus is that they should be synonymous, we will have to rewrite the tag-excerpt and tag-wiki anyway. (In such way that it clearly says that the tag is for both topics.)

5 hours later…
6:32 AM
I didn't feel great about it then, and I don't feel great about it now. But I do think that it should plural, rather than singular. — Asaf Karagila 40 mins ago
@AsafKaragila So you suggest (well-orders)? Or (well-orderings)? Or (well-ordered-sets)? Anyway, it is just a few edits, feel free to go ahead and change the tag in the questions. — Martin Sleziak 37 mins ago
One of the first two options. But I'm generally not in favor of this tag anyway. — Asaf Karagila 36 mins ago
@AsafKaragila I realized that it is not possible to created (well-orders) if (well-order) exists. So I would have to remove the tag, wait 24 hours then add the pluralized tags. Which seems hassle if we are still discussing whether there should be tag for well-ordered sets at all. — Martin Sleziak 33 mins ago
I agree with that. Maybe a moderator can rename it. — Asaf Karagila 32 mins ago
@AsafKaragila Anyway, it would probably helped the discussion if you posted an answer rather than a comment and tried to say why you are against the tag and what do you propose. (Whether you are for removal of the tag for for the synonym with ordinals.) — Martin Sleziak 32 mins ago
Martin, I haven't fully decided yet what I think about it. It's just my "automatic opinion" to start with a negative bias towards new tags. — Asaf Karagila 11 mins ago
Here are the questions which I chose for tag when I created it:
4

It is well-known (forgive the pun) that the axiom of choice (which states that the product of every non-empty family of non-empty sets is non-empty) implies that the proper class of all cardinal numbers is well-ordered, at least in the presence of the ZF axioms. Does the converse hold? If not, i...

7

Given a well-orderable infinite set $A$, can we always say that the set $$\left\{R\in A\times A:\langle A,R\rangle\, \text{is a well-ordering}\right\}$$ has cardinality $2^{|A|}$? How much Choice is required for the proof of this? I believe that where $A$ is countably infinite, we can proceed wi...

13

I tried to write a formal proof for the theorem: $A$ subset of $\mathbb R$ well ordered by the normal order $\implies A$ is at most of cardinality $\aleph_0$. Any suggestions? Thanks.

10

Is there an explicit well-ordering of $\mathbb{N}^{\mathbb{N}}:=\{g:\mathbb{N}\rightarrow \mathbb{N}\}$? I've been thinking about that for awhile but nothing is coming to my mind. My best idea is this: Denote by $<$ the usual "less than" relation on $\mathbb{N}$. Since $\mathbb{N}^{\mathbb{N}}$...

6

There is no known well-order for the reals. Is there a known well-order for any uncountable set? If not, is it known whether or not an axiom stating that only countable sets can be well-ordered is consistent with ZF?

48

So, from what I understand, the axiom of choice is equivalent to the claim that every set can be well ordered. A set is well ordered by a relation, $R$ , if every subset has a least element. My question is: as anyone constructed a well ordering on the reals? First, I was going to ask this questi...

We will see what happens. (Based on outcome of the discussion on meta and when we see whether other users start to use this tag on the main.)
It might be just pluralized. It might be removed. It might be made synonym of ordinals.

10 hours later…
4:51 PM
0

The tag math-jokes was created recently. The tag-wiki is empty, but based on the only question currently having this tag it seems that the intention is that this tag is to be used for questions related to mathematical jokes and questions asking for explanations of such jokes. I can imagine that ...

5:27 PM
After discussion with Asaf was pluralized to .
Thanks to Daniel Fischer.
in Math Mods' Office, 5 mins ago, by Daniel Fischer
@MartinSleziak exists now.
I copied both the tag-excerpt and tag-wiki.
Still, this remains true.
16 hours ago, by Martin Sleziak
If the consensus is that they should be synonymous, we will have to rewrite the tag-excerpt and tag-wiki anyway. (In such way that it clearly says that the tag is for both topics.)

6:22 PM
Currently there is only one question with the tag .
49

So, from what I understand, the axiom of choice is equivalent to the claim that every set can be well ordered. A set is well ordered by a relation, $R$ , if every subset has a least element. My question is: as anyone constructed a well ordering on the reals? First, I was going to ask this questi...

Perhaps adding it later to some of the questions mentioned above will not do much harm. (Maybe it could even remind some users the existence of the post on meta.)
But probably we should not add it to too many questions until we decide about the tag in one way or the other.

6:58 PM
I vote for removing it. With its current name, it's an open invitation to garbage. It might be useful to have a tag called something like "joke-explanation" or so, but even a tag wiki [nobody reads those] wouldn't save its current name. — Daniel Fischer ♦ 24 mins ago
Re: Nobody read do. I do. Typically when I am in doubt whether some tag applies to a question at hand or not. (And I think if some tag was not discussed on meta, then the tag-wiki is typically what decides which questions belong there and which not. Of course, in many situations it is a judgement call, but at least the tag-wiki gives some kind of guidance.) — Martin Sleziak 14 mins ago
Regulars of this thread don't count ;) Of course you and Asaf and Najib, and probably a dozen or two others read tag wikis. I sometimes do, too. But in the grand scheme of things, we are nobody - a small village of Gauls trying to keep the multitudes of the Roman legions in check. But without a magic potion. — Daniel Fischer ♦ 3 mins ago
I definitely agree that most of the users probably ignore the tag-wikis and tag-excerpts (despite the fact that they are shown when the tag is being added). But I still think that it is better if information about correct usage is in the tag wiki, than when it not given anywhere. At least I have some link which I can mention in comment or edit summary to give some explanation why the questions had to be retagged. We digressed from the original topic of this post - if needed, we can continue the discussion in chat. — Martin Sleziak 14 secs ago

7:20 PM
Of course, a bad(ly named) tag with tag-wiki is better than one without. No doubt about that. But a name that is less likely to be misinterpreted is still better. — Daniel Fischer ♦ 25 secs ago