Do we have $|\mathcal P(X)|=|X^X|$ in ZF?
2342
How does equality $\mathfrak{m}^\mathfrak{m} = 2^\mathfrak{m}$ in $\sf{ZF}$ relate to the axiom of choice?
34924
What is the domain of $x^x$ as a real valued function?
81063
If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.
31303
If $p\in\Bbb Z[X]$ show that: $ \max\limits_{x\in [0,1]}\left|p(x) \right| > \frac{1}{e^{n}}. $
44259
Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)
148790
Basic question about proofs with the goal $\exists x P(x)$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
24107
Bijection $f:\mathcal{P}(A)\to(A\to \{0,1\})$
31389
consistency of ZF\{Power Set axiom}
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
79734
Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
139930
Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
112049
How many elements does $\mathcal{P}(A)$ have?
72621
ZF: Difference between POW and SEP?
81873
Is $(X,\mathcal T)$ necessarily an indiscrete space?