query: If card(A) > card(B) then there is no surjection from B onto A, w/o AC.
positive_passages.docid: 154594
positive_passages.text: Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
negative_passages.docid: 53101
negative_passages.text: Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
negative_passages.docid: 89535
negative_passages.text: fake proof of $\forall a. \forall b. a = b \to 1 = 0$
negative_passages.docid: 62172
negative_passages.text: Why does $-b < a < b \iff |a| < b$?
negative_passages.docid: 139841
negative_passages.text: Proving $A\setminus(B\setminus C)$ is not equal to $(A\setminus B)\setminus C$
negative_passages.docid: 87238
negative_passages.text: $(1 2)(3 4)$ does not commute with any nonidentity element of odd order in $A_5$.
negative_passages.docid: 43462
negative_passages.text: Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
negative_passages.docid: 46748
negative_passages.text: If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
negative_passages.docid: 131592
negative_passages.text: Finite choice without AC
negative_passages.docid: 99631
negative_passages.text: Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
negative_passages.docid: 98963
negative_passages.text: Prove that neither $A$ nor $B$ is divisible by $5$
negative_passages.docid: 41044
negative_passages.text: Equivalence of $a \rightarrow b$ and $\lnot a \vee b$
negative_passages.docid: 130381
negative_passages.text: bijection from $(a,b)$ to $\Bbb R$
negative_passages.docid: 5639
negative_passages.text: No \xrightrightarrow[a]{b}?
negative_passages.docid: 136538
negative_passages.text: How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
negative_passages.docid: 125161
negative_passages.text: Why is the Cartesian product of $A$ and $\varnothing$ empty?
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$