Suppose there exist infinite subsets $X_1, . . , X_n$ of F such that f($x_1, . . , x_n$) = 0 for all ($x_1, .. , x_n$) ∈ $X_1 × · · · × X_n$.
33696
A polynomial is zero if it zero on infinite subsets
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
10472
Is every set a subset?
79925
Infinitely many values of $x$ that satisfy the equations
64905
Let $f \in C [a,b]$ such that $\forall x\exists y$ such that $|f(y)| \leq \frac{1}{2}|f(x)|$. Prove that $\exists c\in [a,b]$ such that $f(c) = 0$.
41661
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists
93771
Prove that for any set $A$ there is some $x \notin A$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
22131
Prove if nonempty $K \subset\mathbb{R}$ is compact, then both sup $K$ and inf $K$ exist and are elements of $K$.
40524
Let $A \subseteq (0,\infty$) such that $\inf A>0$. Let $\frac{1}{A}=\{\frac{1}{a},a\in A\}$. Prove that $\sup \frac{1}{A}=\frac{1}{\inf A}$.
111723
Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
81843
Sequences of sets property
5313
Existence of how many sets is asserted by the axiom of choice in this case?
2287
If a set is linearly independent, a finite subset of that set is also linearly independent