query: Prove $\mathbb{Z}^n$ is countable.
positive_passages.docid: 157513
positive_passages.text: How can I prove that these sets are countable infinite?
negative_passages.docid: 138026
negative_passages.text: To show that $n!f(x) \in \mathbb{Z}[x]$
negative_passages.docid: 83001
negative_passages.text: Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 88904
negative_passages.text: Help with a proof. Countable sets.
negative_passages.docid: 157081
negative_passages.text: The cartesian product of a finite amount of countable sets is countable.
negative_passages.docid: 99656
negative_passages.text: Prove that the set of all algebraic numbers is countable
negative_passages.docid: 12472
negative_passages.text: Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
negative_passages.docid: 32795
negative_passages.text: Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 128437
negative_passages.text: How to prove that a finite set is countable
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: 151295
negative_passages.text: Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
negative_passages.docid: 2269
negative_passages.text: Proof that the real numbers are countable: Help with why this is wrong
negative_passages.docid: 90239
negative_passages.text: $\mathbb{Z} \times \mathbb{Z}$ is cyclic.
negative_passages.docid: 43268
negative_passages.text: How to prove that the set of rational numbers are countable?
negative_passages.docid: 41192
negative_passages.text: Neatest proof that set of finite subsets is countable?