query: Is there a relation between card(P($\mathbb Q$)) and card($\mathbb R$);
positive_passages.docid: 41052
positive_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 93017
negative_passages.text: Isomorphism between $\Bbb R$ and $\Bbb R(X)$?
negative_passages.docid: 65379
negative_passages.text: Deriving $\neg R$ from $\{R↔(R∨(P∧¬P)), R↔¬P, ¬P→(P↔(Q→Q)), P→Q\}$
negative_passages.docid: 51687
negative_passages.text: Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
negative_passages.docid: 53432
negative_passages.text: What is the algebraic closure of $\mathbb F_q$?
negative_passages.docid: 138283
negative_passages.text: $|(a,b)| = |\Bbb R|$ ? Cardinality of any open interval
negative_passages.docid: 139064
negative_passages.text: Show by using logical connectives laws that $(P\to Q) \land (Q \to R) $ is equivalent to $(P \to R) \land [(P \iff Q) \lor (R \iff Q)]$
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 137422
negative_passages.text: $\mathrm{card}(\mathbb{Z}^n/M\mathbb{Z}^n) = |\det(M)|$?
negative_passages.docid: 36325
negative_passages.text: Embedding ordinals in $\mathbb{Q}$
negative_passages.docid: 94421
negative_passages.text: Why $P(A) \cup P(B)$ is not equivalent to $P(A \cup B)$
negative_passages.docid: 17670
negative_passages.text: If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 57037
negative_passages.text: How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
negative_passages.docid: 64140
negative_passages.text: Find a bijection from $\mathbb R$ to $\mathbb R-\mathbb N$
negative_passages.docid: 152856
negative_passages.text: Using $p\supset q$ instead of $p\implies q$
negative_passages.docid: 21035
negative_passages.text: Clarifying on how if p,q is logically equivalent to p only if q