The document discusses a quasi order on the set of integers defined by the less-than relation, where one integer is less than another if it divides it. It provides an example of a quasi order based on divisibility, where 2 is less than 8 because 2 divides 8, and 18 and 24 are unrelated because neither divides the other.

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13. The less-than relation on the set of integers I is a quasi order.
EXAMPLE:

15. EXAMPLE:
Let P = 1, 2, 3, … is ordered by divisibility.
2-----8 ( Since 2 divides 8, 2 precedes 8, hence 2< 8)
18-------24 ( 18 does not divide 24, and 24 does not divide 18, hence 18 ∥ 24. )