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Dec
16
comment Skolem Hulls in $H_{\omega_2}$
I answered this question on MO at mathoverflow.net/questions/158293 .
Dec
16
comment “constructible but not definable”
In connection with the last line of the question: It's possible for a set to be definable (without parameters) in some $L_\beta$ yet not be definable (without parameters) in $L$. The point is that $\beta$ might not be definable (without parameters) in $L$.
Dec
16
answered If $B$ is a model for the set of positive consequences of $\Gamma$, then there's $A \subseteq B$ such that $A \models \Gamma$
Dec
16
answered A question in character theory of finite groups
Dec
13
comment If $f$ and $g$ are continuous, then max(f, g) is continuous and differentiable
The part of the question after "So far I'm thinking" looks to me like an attempt at "proof by pun". You're talking there about the max of a function $f$ on an interval, the value $f(c)$ that is $\geq$ all the other values $f(z)$ for the same $f$ and other $z$'s. The problem, on the other hand, concerns the max (or min) of two functions $f$ and $g$ which is a function whose value at any $x$ is the larger of $f(x)$ and $g(x)$, with no reference to any other $z$'s. Although "max" occurs in both, it's applied in entirely different ways.
Dec
13
comment Priority in operations has an axiom or law that justify it?
The convention for division is, in my opinion, nonexistent. I would not write a double division without parentheses.
Dec
13
comment Absolute continuity and Hilbert Space
The original version, which can be seen by clicking the word "edited" below the question, had $f(x)g(x)$ in the numerator.
Dec
13
comment Priority in operations has an axiom or law that justify it?
In the usual set-up, such things are just notational conventions, not axioms. In principle, one could introduce things like the triple product $abc$ as a separate primitive notion and then add $abc=(ab)c$ as an axiom, but I'm not aware of anyone's ever having done that (and it seems a waste of time to introduce a new notation and immediately declare it equivalent to a pre-existing notation.)
Dec
8
comment Trouble Understanding Proof About Polynomials
@fYre Your comment doesn't make sense to me. My answer was about one single prime, namely $p$. This one prime is the "same value" mentioned in my answer and in the second block of quoted material in your question. I don't see how you got to "an infinite number of primes" from any of this.
Dec
8
answered Trouble Understanding Proof About Polynomials
Dec
7
comment About multiplying two essential singularity containing functions
I think the term "essential singularity" is used only for single-valued functions. That would exclude the logarithm, which is a good thing because, in contrast to what Picard's theorem says about essential singularities, the logarithm does not take all but 3 values in every neighborhood of $0$.
Dec
7
answered Questions regarding well formed expressions in the Theory of types
Dec
7
comment Is the complex projective plane a compact manifold with or without boundary (closed manifold)?
Yes it's a closed manifold. Check the definition of the Poincaré conjecture in dimensions $>3$. In particular, check the hypotheses, which concern more than just the fundamental group.
Dec
7
comment Confused about transfinite induction
In the definition of $B$, the phrase "linear span of their predecessors" is ambiguous. I took it to refer to predecessors in $B$, in which case the definition of $B$ uses transfinite induction but the proof that it spans does not. You (apparently) took it to mean predecessors in $V$, in which case the definition of $B$ doesn't need induction but the proof that it spans does.
Dec
6
comment Confused about transfinite induction
I don't think you need transfinite induction or anything like it to prove that $B$ spans $V$. Given any vector in $V$, it is $v_\beta$ for some $\beta$. Either it's a linear combination of earlier elements of $B$, in which case it's a linear combination of $B$, or it's an element of $B$, in which case it's again (trivially) a linear combination of $B$.
Dec
6
comment Prenex form of the power set axiom
Concerning "you need to treat it as $(\phi\implies\psi)\land(\psi\implies\phi)$": Alternatively, you could treat it as $(\phi\land\psi)\lor((\neg\phi)\land(\neg\psi))$. But it would still be the case that "the result will be a mess".
Dec
5
answered Is the cardinality of the set of all isolated points in a second countable metric space at-most $\aleph_0$?
Dec
1
comment How can a set contain itself?
The first sentence in the question "... obviously makes the assumption ..." is wrong. Russell's question makes sense whether or not there are sets that contain themselves. In fact, in some set theories (like Quine's "New Foundations") there are such sets (like the set of all sets), while in other set theories (like ZF) there are no such sets.
Dec
1
answered An example of an ultrafilter
Nov
29
answered Clarifications for linearity of expectation