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Jul
20
awarded  Yearling
Jul
17
comment Cardinality of universal set?
@MaliceVidrine - Thanks for the clarification.
Jul
17
comment Cardinality of universal set?
@AsafKaragila - IIRC, it is only NF plus the infinity axiom (i.e., the existence of infinite sets other than the universal set) whose consistency is an open problem.
Jul
17
revised Cardinality of universal set?
Oops: fix per comment of Asaf
Jul
17
comment Cardinality of universal set?
@Asaf: Oops - both NF and NF(U) in my answer should be qualified with 'hereditarily finite'. I'll change that in a moment.
Jul
17
revised Cardinality of universal set?
Oops: fix per comment of Asaf
Jul
17
comment Why do we need truth functional completeness?
Stranger: That is truth-functional completeness, not expressive completeness. Expressive completeness is something different, to do with axiomatising a theory, which says in one way or another that everything in the theory is represented in the axiomatisation.
Jul
17
comment Why do we need truth functional completeness?
Could you say what definition of expressive completeness you are using? There are alternative ways of formulating it.
Jul
17
answered Cardinality of universal set?
Jul
17
comment A question about HOD
...What is HOD?
Feb
18
awarded  Notable Question
Jan
13
comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$?
@epimorphic - I'm sorry: I managed to confuse myself about what was going on here; it is clear that Annix is not disposed to summarise the problems with his/her answer. You could provide an answer that starts with Annix's attempt at a solution, summarises your comments above to shows why the definition of dual numbers is incoherent, and concludes by saying Steven is right. (If you like, you could just cut and paste your last comment, and I'll fill in the rest.)
Jan
10
comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$?
+1: In view of the fact that, in comments, the qn of @epimorphic, ´What are i, j, and ϵ?´, has been answered, this answer is useful and concise. It would be improved further if the use Anixx has put these glyphs to were explained in the body of the answer.
Jan
9
comment Is $0$ a natural number?
@Annix: I'm not sure why you wrote this comment. Are you claiming ignorance, authority, or something else altogether?
Jan
9
comment Solutions to functional equation $f(f(x))=x$
-1: flippant, incomplete. Your answer does not show that the class with this symmetry has any members other than those in the question
Dec
9
awarded  Caucus
Dec
9
comment In plain language, what's the difference between two things that are 'equivalent', 'equal', and 'identical'?
With ZFC, bijectivity is the same as having same cardinality, but often we care about equivalence as ordinality. If we care about "sets as trees", then bare equality is on topic. (+1: "types")
Sep
9
awarded  Good Question
Jul
20
awarded  Yearling
Jul
2
awarded  Curious