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13h
comment example of multiplication of ordinals with infinite cardinality with larger value on right where we dont' take the max?
That will happen if the second factor is a limit ordinal, but not otherwise. For instance, $2\cdot(\omega+1)=\omega+2$.
14h
revised Wild automorphisms of the complex numbers
Updated dead link to Paul Yale’s paper.
14h
comment example of multiplication of ordinals with infinite cardinality with larger value on right where we dont' take the max?
If you’re talking about ordinal arithmetic, $\omega$ and $\omega^2$ have the same cardinality, both being countably infinite, and their product is $\omega^3$.
15h
answered Boolean algebra consensus theory
15h
revised Limit of $\{a_n\}$, where $a_{n+1} = \sqrt{2+a_n}$
Imported problem from image.
17h
answered An injection from R × {0, 1} to R
19h
answered Perfect powers of successive naturals: Can you always reach a constant difference?
20h
answered Find recursive formula - Question from exam, check my answer
21h
comment Show that a regular space, under a “new” topology, is Tychonoff
@user233397: Excellent; you’re welcome!
23h
answered Proposition $1.3$ in Bondy & Murty's Graph Theory.
23h
comment Problem on elementary logic and set theory
The third sentence of your written proof is incorrect: if $x\notin A\setminus B$, then $x\notin A$ or $x\in B$. You have and instead of the correct or.
23h
comment Minimal posets and chains
It’s not clear what you’re asking. What exactly is the statement that you want to prove (if it’s true)?
1d
comment Lexicographic Orderings of Aronszajn Trees are Aronszajn Lines
@Vinicius: I’ve added a sketch of that part to my answer; there are still a lot of details for you to fill in.
1d
revised Lexicographic Orderings of Aronszajn Trees are Aronszajn Lines
added 767 characters in body
1d
comment $K_n$ as an union of bipartite graphs
@user2820579: You might take a look at this site; if the online text seems readable enough, this page has information on getting hard copies. I find this one more readable than West, though both are pretty daunting simply by virtue of the amount of material. (I’ve never actually seen the Bondy; I’m a topologist, not a graph theorist.) I don’t have any familiarity with possibly more elementary books, I’m afraid. You’re welcome!
1d
comment If $AB$ and $BA$ are defined, then $AB$ and $BA$ are square matrices.
The first assertion is false as stated: $$\begin{bmatrix}1&1\end{bmatrix}\begin{bmatrix}1\\1\end{bmatrix}=[2]\in M_{1,1}\;,$$ and $$\begin{bmatrix}1\\1\end{bmatrix}\begin{bmatrix}1&1\end{bmatrix}=\begin{bmatrix}‌​1&1\\1&1\end{bmatrix}\in M_{2,2}\;.$$ Perhaps you mean that if both products are defined, then both products are square (but not necessarily of the same size).
1d
answered $K_n$ as an union of bipartite graphs
1d
comment Show that $dim(X,\succeq)\leq |X^2|$ when $X$ is finite
@Guilherme: You’re welcome!
1d
comment Show that $dim(X,\succeq)\leq |X^2|$ when $X$ is finite
@Guilherme: For any positive integer $n$ let $a_k,b_k$ ($k=1,\ldots,n$) be $2n$ distinct elements, and set $a_k\le b_\ell$ iff $k\ne\ell$. The resulting partial order is of cardinality $2n$ and dimension $n$. See the example in this Wikipedia article.
1d
comment Show that $dim(X,\succeq)\leq |X^2|$ when $X$ is finite
@Guilherme: I’m not sure what you mean here by a counterexample: counterexample to what, exactly?