New posts in Cardinals

Dimension of vector space, countable, uncountable?

Is there a Partition of $[0,1]$ into closed, countably infinite sets?

On the proof of existence of algebraic closure using Zorn's Lemma in Patrick Morandi's *Field and Galois Theory*

Proof that the number of proofs is countably infinite

Are there uncountable antichains in $\mathcal{P}(\mathbb{N})$

What is $\aleph_0!$?

Is there a set whose power set is countably infinite?

Does there exist an injection $f:\mathbb{R}\to P(\mathbb{N})$ that satisfies these conditions?

Doesn't the unprovability of the continuum hypothesis prove the continuum hypothesis?

Which of the following sets has the greatest cardinality?(Math subject GRE exam 0568 Q.61 )