query: $\vert\mathbb{Q}^m\vert = \vert\mathbb{N}\vert$. Proof
positive_passages.docid: 5803
positive_passages.text: Produce an explicit bijection between rationals and naturals?
negative_passages.docid: 24585
negative_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 92583
negative_passages.text: Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
negative_passages.docid: 157597
negative_passages.text: Homeomorphism between $\mathbb{Q}$ and $\mathbb{Q}(>0)$, and $\mathbb{Q}(\ge 0)$
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 138212
negative_passages.text: Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
negative_passages.docid: 135188
negative_passages.text: Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 137739
negative_passages.text: Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
negative_passages.docid: 92630
negative_passages.text: How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
negative_passages.docid: 31555
negative_passages.text: Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
negative_passages.docid: 46780
negative_passages.text: Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
negative_passages.docid: 72735
negative_passages.text: Understanding the proof of a formula for $p^e\Vert n!$
negative_passages.docid: 127198
negative_passages.text: What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
negative_passages.docid: 36602
negative_passages.text: $a^m=b^m$ and $a^n=b^n$ imply $a=b$