query: $(a,a]=$? Where $a \in \Bbb R$.
positive_passages.docid: 151008
positive_passages.text: Examples of Intervals
negative_passages.docid: 39731
negative_passages.text: The relation $a\theta_n^Sb$ iff $(\forall x\in S^n)\, xa=xb$.
negative_passages.docid: 8787
negative_passages.text: In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
negative_passages.docid: 109764
negative_passages.text: Find the cardinality of the quotient of $\mathbb R$ in respect to R
negative_passages.docid: 98470
negative_passages.text: If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
negative_passages.docid: 33542
negative_passages.text: When is $A- B = B- A$?
negative_passages.docid: 1315
negative_passages.text: Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
negative_passages.docid: 72092
negative_passages.text: If $A^2 = I$, $B^2=I$ and $(AB)^2=I$, then $AB = BA$
negative_passages.docid: 32155
negative_passages.text: Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
negative_passages.docid: 20823
negative_passages.text: If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
negative_passages.docid: 88982
negative_passages.text: Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
negative_passages.docid: 12825
negative_passages.text: Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
negative_passages.docid: 52672
negative_passages.text: Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
negative_passages.docid: 89702
negative_passages.text: Let $R$ be a ring such that for all $a,b$ in $R$, $(a^2-a)b=b(a^2-a)$. Then $R$ is commutative
negative_passages.docid: 91962
negative_passages.text: In a ring $a*a=0$ then $a+a=0$
negative_passages.docid: 131671
negative_passages.text: Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
negative_passages.docid: 133699
negative_passages.text: Proving that there is a bijection between $A$ and $B$.