query: Showing that $\exists f: \mathbb {N} \rightarrow A$ that is injection
positive_passages.docid: 22240
positive_passages.text: Every infinite subset of a countable set is countable.
negative_passages.docid: 146356
negative_passages.text: To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 2072
negative_passages.text: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
negative_passages.docid: 75614
negative_passages.text: Proving that $n|m\implies f_n|f_m$
negative_passages.docid: 67291
negative_passages.text: Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
negative_passages.docid: 49621
negative_passages.text: Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$"
negative_passages.docid: 78698
negative_passages.text: Prove if $f$ has a right inverse function: $f\circ g=id_x$ $\iff$ $f$ is onto $Y$
negative_passages.docid: 138026
negative_passages.text: To show that $n!f(x) \in \mathbb{Z}[x]$
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 21921
negative_passages.text: Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
negative_passages.docid: 148500
negative_passages.text: Understanding this theorem and how to go about proving it surjectivity?
negative_passages.docid: 147546
negative_passages.text: $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable
negative_passages.docid: 40586
negative_passages.text: There exists an injection from $X$ to $Y$ if and only if there exists a surjection from $Y$ to $X$.
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 121395
negative_passages.text: Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
negative_passages.docid: 93964
negative_passages.text: Proving that $f$ is a bijection from $N$x$N$ to $N$.