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18h
answered Number of subsets of $\mathfrak c$ that are different no matter how high you go?
Jul
31
comment Does $G\times H\cong G'\times H'$ imply $G\cong G'$ and $H\cong H'$?
Even simpler, $\mathbb Z_2\times\mathbb Z_1\cong\mathbb Z_1\times\mathbb Z_2$.
Jul
29
comment Which partitions $P$ of $n$ give the row and column sums of some $|P| \times |P|$ $(0,1)$-matrix?
See, e.g., Manfred Krause, A simple proof of the Gale-Ryser theorem, Amer. Math. Monthly 103 (1996), 335-337.
Jul
29
comment Which partitions $P$ of $n$ give the row and column sums of some $|P| \times |P|$ $(0,1)$-matrix?
This is answered by the Gale-Ryser Theorem.
Jul
28
comment Suppose $A\subseteq \mathscr P (A)$. Prove that $ \mathscr P (A)\subseteq \mathscr P ( \mathscr P (A))$
Well, can you prove that if $A\subseteq X$ then $\mathscr P(A)\subseteq\mathscr P(X)$? What happens when you specialize this to $X=\mathscr P(A)$?
Jul
27
comment Is this a typo in Jech's Set Theory?
In short, why don't you just assume that $N$ was supposed to be $M$ and see if it all makes sense that way?
Jul
27
comment Is this a typo in Jech's Set Theory?
I agree that $\{M\cap\lambda:M\in C\}$ makes more sense that $\{M\cap\lambda:N\in C$. The math here is way over my head, so let me ask you: (1) Does $\{M\cap\lambda:M\in C\}$ contain a club set in $[\lambda]^\omega$ (whatever that means)? (2) If so, does the fact that it contains a club set follow from Theorem 8.27 (whatever that might be)? (3) Does the fact (if such it be) that $\{M\cap\lambda:M\in C\}$ contains a club set imply the existence of $M\in C$ with $M\cap\lambda\in S$? If all three answers are yes, you've probably found and corrected a typo.
Jul
27
comment How to show that a curve passes through the origin?
$\frac43x-\frac56x^2$ is not an equation. There is no equals sign.
Jul
22
comment how can I proof that a graph with 2n vertices is bipartite
So how do you prove that a triangle-free graph with $2n$ vertices and $n^2$ edges has no odd cycles? (Other than by using Turan's theorem as in the other answer.)
Jul
21
comment Understanding Spivak's alternative proof that $|a + b|\leq |a| + |b|$
I don't have that book, so I don't know what facts have already been established up to the point you're asking about. To get from $-a\le u\le a$ to $|u|\le a$ we need three facts: $$\text{(1) either }|u|=u\text{ or else }|u|=-u$$ $$\text{(2) }u\le a\implies u\le a$$ $$\text{(3) }-a\le u\implies -u\le a$$ Have any of these three facts already been mentioned?
Jul
19
comment Boolean functions
In your question you neglect to state what condition "such" functions are supposed to satisfy. However, from a comment of yours, I guess you are asking about monotone Boolean functions. Is that right?
Jul
19
comment Graph Theory:Folkman Graph
What is the Folkman graph?
Jul
19
comment Find product limit of this recursively-defined sequence?
I think there';s a typo in your $a_n-1=2(a_n+1)(a_n-1)$ namely the $a_n$ on the right should be $a_{n-1}$?
Jul
11
comment union of two connect sets in particular case
@DanielFischer I think your choice of notation "pick an $A'$" could be a source of confusion, seeing as the OP uses $A'$ for the derived set of $A.$
Jul
10
revised GCD to LCM of multiple numbers
added 48 characters in body
Jul
10
comment Prove that $ |X| \leq |Y| $ if $d(x) \geq d(y) \forall x,y \in E $ in a bipartite graph
@BrianM.Scott OK, thanks.
Jul
10
answered Continuous bijective function between the same topology that is not a homeomorphism.
Jul
1
comment Ball with euclidean metric - mistake in book?
You're right, instead of $x^2+y^2\lt1$ it should be $x^2+y^2\lt1^2.$
Jun
28
answered Find the sum of the first $3n$ terms of a geometric series given the sum of the first $n$ terms is $48$ and the sum of first $2n$ terms is $60$
Jun
25
comment What is the combinatorial proof for the formula of S(n,k) - Stirling numbers of the second kind?
I don't think you mean "$k$ is the number of partitions" because $S(n,k)$ is the number of partitions.