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9h
comment Constructing a Banach space of cardinality $\beth_{\omega+1}$
@AsafKaragila: I did discover the Baire category argument for part (b), but it only got me as far as $|X| > \beth_\omega$. To get $|X| \ge \beth_{\omega+1}$ I had to work harder.
9h
asked Constructing a Banach space of cardinality $\beth_{\omega+1}$
9h
comment $(\beth_{\omega})^\omega=\beth_{\omega+1}$
Oops, let me try that comment again. This is Exercise I.13.33 in the 2013 edition of Kunen's Set Theory. It actually asks you to show a little more: $(\beth_\omega)^\omega = \left|\prod_{n < \omega} \beth_n\right| = \beth_{\omega+1}$.
9h
accepted Constructing a vector space of dimension $\beth_\omega$
10h
comment Weak solution of a parabolic equation when initial and boundary conditions are inconsistent
@jokersobak: For a continuous function $u$ on a set $A$, we say $u$ extends continuously to $B \supset A$ if there is a continuous function $v$ on $B$ with $u=v$ on $A$.
1d
comment Constructing a vector space of dimension $\beth_\omega$
Ah, that's very nice!
1d
comment Constructing a vector space of dimension $\beth_\omega$
I just found this answer on MO which purports to show that $\dim W^* \ge 2^{\dim W}$ whenever $\dim W \ge \aleph_0$. It may take me a little time to digest the Boolean algebra language, though.
1d
asked Constructing a vector space of dimension $\beth_\omega$
1d
comment How can one rigorously determine the cardinality of an infinite dimensional vector space?
Oh right, it still gives us $|V| \le \max(|B|, |F|)$. But $|B| \le |V|$ and $|F| \le |V|$ are immediate.
1d
comment How can one rigorously determine the cardinality of an infinite dimensional vector space?
I edited to fix some typos and hopefully didn't break anything. That said, I am not sure I believe the argument as written. Certainly the map you describe is a surjection from $[B \times (F \setminus \{0\})]^{<\omega}$ to $V$. But I don't think it's an injection. If $v \in B$, don't $\{ (v,3) \}$ and $\{(v,1), (v,2)\}$ both map to $3v$?
1d
comment Eigenfunctions of the Laplacian with imaginary eigenvalue
I seem to have answered a different question. See edit.
1d
revised Eigenfunctions of the Laplacian with imaginary eigenvalue
edit
1d
revised How can one rigorously determine the cardinality of an infinite dimensional vector space?
fix delimiters
1d
revised Understanding mathematical texts
edited tags
2d
answered Weak solution of a parabolic equation when initial and boundary conditions are inconsistent
2d
comment What is the meaning of “fix” in field theory?
Yeah, wouldn't the second case normally be stated as "$S$ is invariant under $\sigma$"? Do you know of a reference in which "fixed" is used in the second sense?
2d
revised More preliminaries of the Martingale Convergence Theorem
proof of fact for analytic functions
2d
comment More preliminaries of the Martingale Convergence Theorem
@1234: Actually I was mistaken - the statement I gave before is not actually correct for $n > 1$. But the statement we need is still true. See my edit.
2d
revised More preliminaries of the Martingale Convergence Theorem
proof of fact for analytic functions
2d
comment I need help understanding this proof about convergence in distribution
@tom: $e^{-x}$ actually. Fixed, thanks.