Prove that the interval $(0,1)$ and the Cartesian product $(0,1)\times(0,1)$ have the same cardinality.
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
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 $\mathbb R^1$
25553
elementary set theory (cartesian product and symmetric difference proof)
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
41783
Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
51206
If $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.
27855
Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
31318
Cardinality of cartesian square
88155
Show that $[0, 1)\times[0, 1)$ is homeomorphic to $[0, 1]\times[0, 1)$ but not to $[0, 1]\times[0, 1]$.
18023
The direct sum $\oplus$ versus the cartesian product $\times$
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
150790
Prove two sets have same Cardinality by writing down bijection
47639
Uncountable Cartesian product of closed interval
106884
Is there a continuous bijection between an interval $[0,1]$ and a square: $[0,1] \times [0,1]$?
150064
Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$