query: Is it true that the set $P$ of all injections $\mathbb{N} \to \mathbb{N}$ is equal to the set $\mathbb{R}$
positive_passages.docid: 28692
positive_passages.text: Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 84437
negative_passages.text: Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
negative_passages.docid: 83291
negative_passages.text: Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
negative_passages.docid: 79734
negative_passages.text: Is every sub-lattice of $\mathcal P(X)$ isomorphic to a sub-lattice of $\mathcal P(X')$ containing singleton sets?
negative_passages.docid: 109610
negative_passages.text: Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
negative_passages.docid: 98897
negative_passages.text: Proving that the set of $\nu$ measurable sets $M\subseteq P(X)$ is an algebra
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: 37951
negative_passages.text: proof detail concerning bijection between a set and its power set
negative_passages.docid: 124333
negative_passages.text: A bijection between $\mathbb{N}$ and $\mathbb{P}(\mathbb{N})$?
negative_passages.docid: 145397
negative_passages.text: How to prove that for every $i$, $a_i = i$
negative_passages.docid: 124060
negative_passages.text: Are these subsets of the powerset P(N) countable?
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 101669
negative_passages.text: Cardinality of the Set of all finite subset of $\mathbb{R}$
negative_passages.docid: 18334
negative_passages.text: Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
negative_passages.docid: 64320
negative_passages.text: Prove that if $0<a<Pr(A)$ then there exists $B\subset A$ such that $Pr(B)=a$
negative_passages.docid: 31391
negative_passages.text: bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$