So this textbook I'm working through is claiming that x ∗ y ≥ 0 on the Integers is a transitive relation, however this seems clearly wrong. Let x ~ y and y ~ z. If x < 0, y = 0, and z > 0, then clearly x ~ z is false, and would not be a part of the relation. What am I missing here?
Asked
Active
Viewed 77 times
2
-
8As far as I can tell, you're not missing anything. – PrincessEev Oct 18 '21 at 21:37
-
5The relation would be transitive if it was $x\cdot y>0,$ but not as $x\cdot y\ge 0.$ – subrosar Oct 18 '21 at 21:40
-
3It's a transitive relation on the non-zero integers. Perhaps this is what your textbook claims? Or perhaps the relation is $x\cdot y>0$? – TonyK Oct 18 '21 at 21:42
-
Avoid the use of ∗ to denote multiplication. That just cause confusion. – jjagmath Oct 18 '21 at 22:53