Prove that the interval $[0,1)$ and $[0,2) \cup [3,4)$ have the same cardinality
49440
Prove that the interval $ \ [0,2)$ and $ \ [5,6) \cup [7,8)$ have the same cardinality
85099
How many subsets of $\mathbb{N}$ have the same cardinality as $\mathbb{N}$?
73850
Cardinality of set of functions
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
65768
What is the cardinality of the set of the empty set?
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.
106884
Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
22232
Proving that cardinality of the reals = cardinality of $[0,1]$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
117478
Prove that $\mathbb{R}$ and the interval $(0, \infty)$ have the same cardinality.
146664
The union of two linearly independent subsets
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
143735
Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
108394
Proof of that every interval is connected
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
158399
Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
82628
Cardinality of a set of closed intervals