query: How do you prove that $<$ is transitive?
positive_passages.docid: 143646
positive_passages.text: Is it possible to prove reflexive, symmetric and transitive properties of equality and the transitive property of inequality?
negative_passages.docid: 80009
negative_passages.text: Prove that $| |a|-|b| | \le |a-b|$
negative_passages.docid: 138436
negative_passages.text: How to prove reflexivity, symmetry and transitivity for the following relation?
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: 17032
negative_passages.text: If $ab=ba$, Prove $a^2$ commutes with $b^2$
negative_passages.docid: 108742
negative_passages.text: Proving commutativity of addition for vector spaces
negative_passages.docid: 52118
negative_passages.text: Where we have used the condition that $ST=TS$, i.e, commutativity?
negative_passages.docid: 143072
negative_passages.text: Proving $|\sin x - \sin y| < |x - y|$
negative_passages.docid: 8456
negative_passages.text: Prove that $SL(2,\mathbb{R})$ acts transitively on the upper half plane
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$
negative_passages.docid: 99346
negative_passages.text: Prove a result on transitive group actions.
negative_passages.docid: 1707
negative_passages.text: How does one prove that addition on $\mathbb{R}$ is associative?
negative_passages.docid: 68781
negative_passages.text: proving if $a \le b$ then $\sup(A) \le \inf(B)$
negative_passages.docid: 18462
negative_passages.text: Transitivity check vs. Transitive Closure
negative_passages.docid: 81868
negative_passages.text: How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
negative_passages.docid: 71977
negative_passages.text: Give an example of a relation R on $A^2$ which is reflexive, symmetric, and not transitive
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof