172,047 reputation
16230470
bio website boolesrings.org/asafk
location Israel
age 29
visits member for 4 years, 3 months
seen 15 mins ago

Ph.D. student in the Hebrew University of Jerusalem.

Set theorist to-be.


19m
revised How can a function with asymptotes be defined as a mapping?
edited tags
1h
answered Let : X → Y be a function. Show that if f is injective then f(A ∩ B) = f(A) ∩ f(B) for sets A ⊆ X and B ⊆ X.
1h
comment Defeating Russell's paradox
You are reading my comments backwards. Your answer begins with the sentence "Russell's paradox is based on the naive assumption that the set of all sets does exist.", and this means that if a set theory has a universal set, then it will be susceptible to Russell's paradox. I am just saying that this is not true, and that this first sentence is very misleading. There are set theories which have universal sets, but Russell's paradox fail there. I'm not quite sure what else to say about that, since you seem to ignore my comment and read them otherwise, so I'll stop now. Have a nice day!
1h
comment Defeating Russell's paradox
Your answer hints that this is the basis for the paradox. It is not. It has nothing to do with the paradox, as shown by the fact that there are axiomatic set theories in which there is a universal set. If you meant something else, please write you meant.
1h
comment Defeating Russell's paradox
Because the Russell paradox is not based on the assumption that the set of all sets exists. If so, why doesn't it appear in Quine's New Foundations where there is a set of all sets?
2h
awarded  Nice Answer
2h
comment Is there really anything wrong with Bourbaki's Set Theory?
I didn't write anything about it being wrong or not. I didn't read the book past the first couple of pages that seemed overly complicated to me (even if you want to be strictly formal about set theory). You explained that you chose Bourbaki as a candidate because you wanted an axiomatic "super abstract" book about set theory. I'm not sure what "super abstract" would be. But regardless to that, modern axiomatic set theory has changed its characteristics since the 1960s making the book obsolete regardless to any mistakes.
3h
comment Is there really anything wrong with Bourbaki's Set Theory?
Old and outdated.
3h
revised Counting sets and adding an element
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4h
comment Is there really anything wrong with Bourbaki's Set Theory?
Note that none of the members of Bourbaki was a set theorist. And that the developments in axiomatic set theory since the 1960's make pretty much any book about axiomatic set theory written before 1970 obsolete. If you are looking for a rigorous approach, pick up Kunen's 1983 "Set Theory", or Halbeisen's "Combinatorial Set Theory" (which also has a free edition on the author's website). Those do a very good job in presenting modern axiomatic set theory.
5h
comment Is the set of all cardinals smaller then a strongly inaccessible cardinal closed?
It's not clear, and it's even less clear what it has to do you with your question in the first place.
6h
comment Defeating Russell's paradox
No, Russell's paradox is based on the naive assumption that every property defines a set. In particular this assumption means that there is a set of all sets, since "$x$ is a set" is an example of such property.
6h
revised inductively defined group statements
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10h
revised An increasing sequence of compacts
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10h
comment How to deal with probability problems in proper class sample spaces?
Ali, I don't know if every difficult question is inherently worth asking. Idle curiosity is fine, but to what end? For what it's worth, I [very] vaguely recall some probabilistic arguments on countable models of $\sf ZF$. I think it's a theorem of Sacks, but I don't remember. I'll see if I can find a reference later today.
10h
comment Why isn't this a valid argument to the “proof” of the Axiom of Countable Choice?
In addition to what Andres said, let me remark that it'd be best if you first come up with an actual answer compared to your very first write up here. I was considering to flag it as "low quality", but when I came to do so, I saw that you added something. This is particularly true since there is no "race" over this question, it's almost two years old, and was dormant for the most of that time. First thing about your answer, see if it satisfies you, then post it (especially for very old questions).
11h
comment Infinite prisoners with hats — is choice really needed?
@Henning: Of course I don't expect them to know about The Prisoner (despite the fact it is still the best TV show ever made), but last year only two were watching True Detective, if you want to talk about contemporary pop culture. And they are not at all versed in good pop culture. It's horrible too, since I make plenty of references to TV and movies as I go along (in real life too). I keep calling them Philistines, but they don't know what I mean either (which shows lack of Bob Dylan familiarity, because that's where I learned it)... :-P
19h
comment Infinite prisoners with hats — is choice really needed?
@Henning: See Hans' comment. Thank you very much Hans!
21h
comment Show that a set defined on a arc segment is closed
Just because something includes a set doesn't mean it has anything to do with set theory.
21h
comment Show that a set defined on a arc segment is closed
Why do you think this is a question related to elementary set theory?