Reflexive Relation/Examples/Divisibility on Natural Numbers

Example of Reflexive Relation

Let $\sim$ be the relation on the set of natural numbers $\N$ defined as:

$x \sim y \iff x \divides y$

where $\divides$ denotes divisibility.

Then $\sim$ is reflexive.


Proof

This is demonstrated in Divides is Reflexive.

$\blacksquare$


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reflexive relation
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reflexive relation
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