Can somebody explain why the interval $\left ( 0,1 \right )$ is not countable?
6681
How does Cantor's diagonal argument work?
62542
Why is the empty set considered an interval?
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
148507
Why an open set in $R^n$ might not be written as countable union of disjoint open intervals?
1318
What is wrong with this proof that the power set of the natural numbers is countable?
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
9696
The interval [0,1] andd [3,5] are equivalent. Is my proof correct?
122048
why is the set of all binary sequences not countable?
125233
Why is an open interval not a compact set?
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
138052
How to work out the limit of  this bounded sequence?
40463
Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$
46967
What is wrong with this proof that the power set of natural numbers is countable?
39406
Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
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 $\mathbb R^1$
98377
How can I prove this limit doesn't exist?
55978
Prove that for every countable ordinal $\alpha$, $\alpha\times[0,1)$ is order isomoprhic to $[0,1)$