we want to prove that $(n,n+1) \cap \mathbb{N}$ is empty
51928
Use an induction argument to prove that for any natural number $n$, the interval $(n,n+1)$ does not contain any natural number.
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
110635
Proving $\mathbb{N}^k$ is countable
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
151295
Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
10107
Prove $A\cup (A\cap B) = A$
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
34099
Proving that the empty set is unique