Popopo

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A student in Philosophy but also curious in many fields.

I don't know,

But I want to know.

	609 reputation	bio	website		visits	member for	11 months
226 badges		location	Pop Star, MathCraft		seen	1 hour ago

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Apr 16	comment	Can we conclude that $\|\prod_{\xi \in Ord, \xi=1}^{\xi<\alpha}\xi\|=2^{\|\alpha\|}$ for all infinite ordinal $\alpha$ in $\mathsf{ZFC}$? @Apostolos Thank you, that's all right.
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? Thank you for your suggestion.
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? Thank you very much. Besides, a little tip: when $\alpha=\beta+1$ then $\Gamma(\aleph_\alpha)$ should be $2^{\aleph_0}\aleph_{\beta}^{\|\beta\|}$.
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? I'm sorry that I have made another error: this product is the cardinal product of all positive cardinals smaller than $\aleph_\alpha$ whereas in the lemma 1 I had considered it as the cardinal product of all positive ordinals smaller than $\aleph_\alpha$.
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? I'm sorry about that...
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? @AsafKaragila Sorry, in that time I have mistook the definition of beth numbers (mistook that $2^{\aleph_\alpha}=\beth_{\alpha+1}$).
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? Thank you, it's amazing.
Apr 16	comment	Can we conclude $\prod_{\kappa \in Crd, \kappa=1}^{\kappa<\aleph_\alpha}\kappa=2^{\aleph_\alpha}$ in ZFC? @CliveNewstead Thanks, I'm going to fix it.
Apr 12	comment	Entropy: Is $H(X_{1},X_{2}) = H(X_{1})$ true? You are welcome.
Apr 10	comment	Given a relation $R$, is it reflexive? Symmetric? Transitive? $R$ is not transitive. Let $a=6,b=15,c=35$, you can easily check them.
Apr 7	comment	Difference between “Live” and “Define” @suissidle The word `let` sometimes used as `define` but informally. What's more, it sometimes used as `assign`, e.g. let $x=0,y=1$.
Apr 6	comment	What's the remainder of a natual number divided by lcm(m,n)? Thank you, I have improved my question.
Apr 6	comment	How to deal with infinite continued fractions in formal language? I see, generally infinite continued fraction $[x_0;x_1,\dots]$ is a (partial) function in ${\mathbb R}^{{\mathbb R}^{\omega}}$, which maps some infinite sequences $\langle x_0,x_1,\dots\rangle$ of reals to a real number.
Apr 5	comment	What's the remainder of a natual number divided by lcm(m,n)? Yes, I understand. Thank you.
Apr 5	comment	How to deal with infinite continued fractions in formal language? @MarianoSuárez-Alvarez I found it is hard to express limits in first-order language either... We need to express supremum and infimum of sets(possibly infinite), so does it require higher-order language?
Apr 4	comment	Why don't we study algebraic objects with more than two operations? @ChrisEagle Okay, I see.
Apr 4	comment	Why don't we study algebraic objects with more than two operations? @ChrisEagle Why fields can not be treated as universal algebras?
Mar 30	comment	Are there rules in the useage of prepositions in Math? @TaraB I think that the 'form word' I expressed is 'syntactic expletive', but in precisely in this post they are indeed prepositions.
Mar 30	comment	Are there rules in the useage of prepositions in Math? Yes, you are right.
Mar 27	comment	What is the correspondence between the semantic compactness of logics and the compactness of Stone spaces? Okay, let $\mathbf 1=Cn(\emptyset)$ is well. Both $\mathfrak F(\mathcal L)$ and $\mathfrak F(\mathcal L)/ \Leftrightarrow$ can be complete lattice.