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May
7
comment what does function from a set to its power set mean?
@Memming: the difference is probably that rahul got tired of writing dashes.
May
7
comment what does function from a set to its power set mean?
I don't understand the downvote. Isn't this exactly the kind of question we want to answer in the elementary set theory tag?
May
7
comment what does function from a set to its power set mean?
Just define $f(1) = \{2,3\}, f(2) = \{1,2,3\}, f(3) = \{3\}$. The point is that functions don't have to be defined from some "rule"; they can be defined in an almost completely arbitrary fashion. If you pick any three elements of $P(A)$ (even allowing repetitions!) you can make a function which maps to those elements.
May
7
answered what does function from a set to its power set mean?
Apr
30
comment Set Theory Proof: Valid or not?
I don't understand your notation in 1, 2, and 3. Usually set theorists (and mathematicians in general) use { ... | ... } to mean a particular set, which is like a mathematical object; in a proof, you need to be writing statements (about mathematical objects).
Apr
27
comment The genus of a certain kind of cubic
And a singularity is a double point or cusp?
Apr
27
comment The genus of a certain kind of cubic
So, if $a_3$ is nonzero in my question, then the curve is not elliptic and hence has genus $0$?
Apr
27
comment The genus of a certain kind of cubic
Are you saying that for the curve to have positive genus it must be of the form $y^2 = x^3 + ax + b$, with $a$ and $b$ rational? Or is "genus $1$" the definition of "elliptic"?
Apr
26
asked The genus of a certain kind of cubic
Apr
17
asked Does there exist a quadratic generalization of the continued fraction approximants?
Mar
10
comment Jech's Set Theory logic prerequisites
@Nectric: I'd say Jech's book is actually fairly self-contained; but its scope is far too large for it to be anything other than a reference. Plus, its treatment of certain topics (forcing in particular) is not what I would want for a beginner.
Mar
10
answered Jech's Set Theory logic prerequisites
Mar
6
answered Existence of an uncountable set of sequence
Feb
24
revised Initial segments of trees
Not all subsets are initial segments.
Feb
21
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Feb
18
comment Questions of $\mathbb{P}$-name for a set and functions
Which $p$ are you talking about in your two questions?
Feb
17
answered Initial segments of trees
Feb
13
comment Question of $\Diamond$ in Generic Extension
Apply $\diamondsuit$ to the $\mathbb{P}$-names for subsets of $\omega_1$? (By the ccc, you can code such a name as an $\omega_1$-sequence of countable subsets of $\mathbb{P}$.)
Jan
28
comment Measurability Question?
@anthonyquas: isn't it pretty direct from the definitions? A reverse well ordering is a linear order with no infinite, strictly increasing subset.
Jan
27
comment Measurability Question?
If $X$ is a Polish space and $\mathcal{B}$ is the $\sigma$-algebra of Borel sets, then $S$ looks like it's analytic and hence measurable with respect to any complete Borel measure. I'm not sure that it's not Borel, though.