Given $A_1 = \{\emptyset\}$ and $A_{n+1} = A_n \cup (A_n \times A_n)$ define $A = \bigcup_{i=1}^\infty A_n$, what is $A\times A$?
70940
Homework - set theory infinite union
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
13282
In the category $\mathbf{Set}$ is "the product of an empty set of sets a one-element set"?
139595
Show that $(l_1)^* \cong l_{\infty}$
143003
$\bigcup \emptyset$ is defined but $\bigcap \emptyset$ is not. Why?
130297
$A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
74207
What is $i$ exponentiated to itself $i$ times?
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
21114
$S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
27899
Can we prove the existence of $A\cup B$ without the union axiom?
11961
Why does $\lim_{n \to\infty}a_{n+1} = \lim_{n\to\infty}a_n$?
148234
Express set $[a,b] \cup [c,d]$ as the difference of two intervals
86034
Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?
150166
What is $P([a_1,b_1]\times [a_2,b_2]\times...\times[a_k,b_k])$
123576
Why does $\lim_{n\to\infty} z_n=A$ imply $\lim_{n\to\infty}\frac{1}{n}(z_1+\cdots+z_n)=A$?