I just spotted an old duplicate and, ashamed to admit, seem to have answered them both. Exhibit 1, 2. I have the dupehammers, and could just flip a coin, or let the first stay, as the answers there are a bit more elaborated. Not much to base a decision on. OTOH the question is a bit more verbose on the other one, and it is also a bit older. Soliciting opinions :-)
So I have recently come across the Collatz Conjecture, I know that there no way to prove the conjecture that we know of, but I'm just curious. Does anything weird or different happen to the 4-2-1 cycle if you replace n with an irrational number like π?
A user here has posted four times in little more than a day, urging that this question on whether the equation a=a+1 is true for infinite cardinals without the axiom of choice should be closed/deleted. And they seem frustrated that members of the community are upvoting and voting to reopen. It's not the most elegantly written question, but it's perfectly reasonable, and has attracted a good quality answer.
@JyrkiLahtonen Q1 has a seemingly more detailed answer whereas Q2 has a little more context. Perhaps Merging the answer to Q1 into Q2 and making the original answer to Q2 a wiki?
@JeremyRickard I am this user , and no , I won't reopen it. I am surprised (to say the least) that it is almost reopened since the sense in which $a=a+1$ shoould hold is not clarified at all. Maybe , it was exaggertating that I posted this question multiple times , and I won't do this again since it is apparently pointless anyway. I still think this question should be deleted.
I'm analyzing Korec's paper about the Collatz Conjecture https://dml.cz/bitstream/handle/10338.dmlcz/133225/MathSlov_44-1994-1_8.pdf.
I have some questions about his approach:
U(m,d) corresponds to the cardinality of the set containing the numbers 0<y<2^m such that the numbers of 1's is <= md?
...
@Peter "the sense in which $a=a+1$ shoould hold is not clarified at all" There is nothing that needs clarification. The question states that a is the cardinality of the set A; both "=" and "+1" have completely standard meanings in the context of cardinality. (Note that "cardinality" is not the same as "cardinal" in the context of choiceless set theory - cf. "Scott cardinality.")
@Ѕᴀᴀᴅ @NoahSchweber @Peter @JeremyRickard Just to be clear, I believe that this room should be used to discuss whether or not a question should be handled in a particular way. Discussion is healthy. However, please try to keep it to the content of the questions and answers (e.g. "I don't think the user understand the question" is not okay).
2
I have deleted a couple of comments, which seemed to be a little close to the line.
@Peter It was suggested that you posted the same question in here four times. Please don't do this. Once or twice is fine, but if, after posting the question a couple of times, it remains open, you should take that as representative of the opinion of users of this room. It starts to look like you have an axe to grind.
So I have recently come across the Collatz Conjecture, I know that there no way to prove the conjecture that we know of, but I'm just curious. Does anything weird or different happen to the 4-2-1 cycle if you replace n with an irrational number like π?
