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seen Nov 10 at 19:01

Nov
28
awarded  Necromancer
Oct
23
awarded  Yearling
Sep
30
awarded  Explainer
Sep
27
comment Are any two uncountable sets similar to each other?
@VHP: Is $A \subseteq B$ in your problem?
Sep
27
comment Are any two uncountable sets similar to each other?
Well, any two countable sets are similar because "countable" refers to only one cardinality, and similarity is the definition of being equinumerous. But Cantor's theorem shows you that there's always a properly bigger set if you can form the powerset.
Sep
25
comment What is an axiom schema?
It's usually a set characterized syntactically. They're all alike modulo some relettering of variables and plugging in subformulae in the right spots.
Sep
17
comment Why can't a set have two elements of the same value?
You're on a road trip with three friends, Eiko, Biko, and Shiko. You decide is so much fun that next year you want to go on a trip with Eiko, Eiko, Biko, and Shiko to change things up. Except you don't decide that, because the idea is absurd.
Sep
14
comment Can the logic associative law be applied here?
Well that's the thing here: associativity isn't part of the definition of implication, so if it holds you have to prove it.
Sep
12
comment Adjoint functors for the power set monad
Yes, though I've seen it referred to simply as the "powerset monad". It sounds like there are others I'm not familiar with, though.
Sep
11
comment Adjoint functors for the power set monad
In the powerset monad that I'm familiar with, the contravariant powerset functor is both the $F$ and the $G$, and the counit is the unit in $\mathbf{Set^{op}}$.
Sep
11
comment Can a function be applied to itself?
Since I always have to chime in with things like this, in NF(U) it's easy to construct examples of such functions (NF violates both foundation and Cantor's theorem). Let $g$ be any permutation of $V$, and let $Q$ be $\{\langle f,g\circ f\rangle : f\in Funct\}$. $Q$ is a function itself, hence it's in $Funct$, and therefore a member of its own domain.
Sep
10
comment quantification domain of set theory formulas
Why should it need to?
Sep
3
comment Recommendation on Category theory textbook
I really like ACC, though it should be mentioned it doesn't have quite the breadth of Mac Lane. Though it also covers some concepts I haven't seen in other book-length works.
Aug
30
answered Are $1+ω$ and $ω+1$ isomorphic?
Aug
30
comment Are $1+ω$ and $ω+1$ isomorphic?
Yes, I'm quite familiar with ordinal arithmetic. That wasn't the part that made your comment opaque. Though if you're talking about concatenation of wellorders you may not want to write it as an ordinary union.
Aug
30
comment Are $1+ω$ and $ω+1$ isomorphic?
"Inputed"? (Not trying to be pedantic, actually trying to figure out your comment.)
Aug
30
comment Are $1+ω$ and $ω+1$ isomorphic?
$\mathbb{N}\cup\{a\}$, without further information, isn't necessarily wellordered. One needs to know what happens to the relation $\leq$ when $a$ is added.
Aug
28
comment Models of set theory
Models are something you deal with inside some other theory. You can't reasonably ask for a model of every theory prior to any use of a theory...
Aug
28
comment Sigma-Algebra: Is it an Algebra, Field, or Something Else?
I don't think that's really the most general sense of "an algebra"...
Aug
26
comment Natural and Real sets of numbers, which one is bigger than another?
@enthusiasticstudent: One being a subset of the other isn't enough to guarantee a difference in size. Think about, say, all multiples of three. They constitute a proper subset of the natural numbers, but there's as many of them as there are natural numbers!