query: Prove that $Dom(S \circ R )= Dom (R)$
positive_passages.docid: 22758
positive_passages.text: If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$.
negative_passages.docid: 32772
negative_passages.text: Proving units in a ring
negative_passages.docid: 151803
negative_passages.text: Prove that $R$ is commutative
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 26766
negative_passages.text: Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
negative_passages.docid: 80827
negative_passages.text: Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
negative_passages.docid: 66548
negative_passages.text: proving topological equivalence
negative_passages.docid: 57418
negative_passages.text: How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 7384
negative_passages.text: How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
negative_passages.docid: 25155
negative_passages.text: Suppose $R$ and $S$ are transitive relations on $A$. Prove that if $S \circ R \subseteq R \circ S$ then $R \circ S$ is transitive.
negative_passages.docid: 14158
negative_passages.text: Prove that $R$ is an integral domain $\Leftrightarrow$ $R[x]$ is an integral domain
negative_passages.docid: 8317
negative_passages.text: Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
negative_passages.docid: 50273
negative_passages.text: How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
negative_passages.docid: 28798
negative_passages.text: Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 121886
negative_passages.text: Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$