Symmetric Relation/Examples/Distance Less than 1
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Example of Symmetric Relation
Let $\sim$ be the relation on the set of real numbers $\R$ defined as:
- $x \sim y \iff \size {x - y} < 1$
Then $\sim$ is symmetric and reflexive, but not transitive.
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 7$: Relations