query: Is there a surjection from $\mathbb N$ onto $\prod\limits_{n \in \mathbb N}I_n$?
positive_passages.docid: 75019
positive_passages.text: Infinite Cartesian product of countable sets is uncountable
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: 128108
negative_passages.text: $Y=\prod_{n\in\mathbb{N}}X$.
negative_passages.docid: 77548
negative_passages.text: Given an arbitrary infinite set $S$, how to construct an injection $\mathbb{N} \to S$ with the Axiom of Choice?
negative_passages.docid: 104016
negative_passages.text: Limit point of the set $G= \{1/n: n \in \mathbb N\}$?
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 93923
negative_passages.text: No surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
negative_passages.docid: 6161
negative_passages.text: The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
negative_passages.docid: 68320
negative_passages.text: Infinite Product $\prod\limits_{k=1}^\infty\left({1-\frac{x^2}{k^2\pi^2}}\right)$
negative_passages.docid: 131425
negative_passages.text: Prove that the convergence of $\prod_{n=1}^{\infty} b_n$ implies $\lim_{n→∞} b_n = 1$
negative_passages.docid: 16610
negative_passages.text: Surjectivity of a map from a space to itself
negative_passages.docid: 20437
negative_passages.text: Closed surjection that does not preserve regularity
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 102112
negative_passages.text: Idempotents in $\mathbb Z_n$
negative_passages.docid: 21782
negative_passages.text: Is $\aleph_0 = \mathbb{N}$?
negative_passages.docid: 7802
negative_passages.text: Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer