Let $x \in \mathbb R$. Prove that the $\lceil{x}\rceil$ is unique; that is, prove that there is at most one $n \in \mathbb Z$ with $n − 1 < x ≤ n.$
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
146421
How to prove a total order has a unique minimal element
80212
Suppose that $X$ is a topological space and $x_0\in X$. Prove that $\widetilde{H_n}(X)=H_n(X,x_0)$ for all $n\geq 0$.
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
13398
Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
110310
$|x_{n+1} - x_n| \le C |x_n - x_{n-1}|.$ Prove $(x_n)$ is cauchy
1409
Proving that the given set has at most $2^{n-1}$ elements
100134
Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
77973
How to prove or disprove $\forall x\in\Bbb{R}, \forall n\in\Bbb{N},n\gt 0\implies \lfloor\frac{\lfloor x\rfloor}{n}\rfloor=\lfloor\frac{x}{n}\rfloor$.
149382
Prove that $(0,1) \subseteq\mathbb R$ and $(4,10) \subseteq\mathbb R$ have the same cardinality.
88736
How does the Axiom of Extensionality prove the uniqueness of Specified sets?
42516
If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
76110
Proving that the zero vector is unique