Simplify doesn't simplify some simple inequalities

Question

I have an pair of inequalities joined by Or that I can't get Simplify or FullSimplify to simplify:

Simplify[x > y || x > y + z, Assumptions -> {x > 0, y > 0, z > 0}]
(* x > y || x > y + z *)

when I expected

(* x > y *)

since x > y + z seems to imply x > y when z > 0.

Any ideas on how to get this result? (unless I'm making a boneheaded logical error myself :)

I hadn't considered it an actual bug, but that may be worth a shot. — Chris K, Oct 14, 2016 at 20:45

Community · Accepted Answer · 2017-04-13 12:55:36Z

2

Use Reduce instead.

Reduce[(x > y || x > y + z) && x > 0 && y > 0 && z > 0] 
(* y > 0 && x > y && z > 0 *)

Edit: As suggested by Julien Kluge, using Refine as well produces a cleaner answer.

Refine[Reduce[(x > y || x > y + z), (x | y | z) ∈ Reals] , x > 0 && y > 0 && z > 0]
(* y < x *)

CommunityBot

1

answered Oct 13, 2016 at 21:14

bbgodfrey

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$\begingroup$ This could be further shortened if we use Refine with the same Assumptions as above. $\endgroup$
– Julien Kluge
Oct 13, 2016 at 21:26
2

$\begingroup$ No no. Reduce is nessecary. Refine would only be useful to shorten your output to the expected x>y. $\endgroup$
– Julien Kluge
Oct 13, 2016 at 21:32
$\begingroup$ Both of these functions are unfamiliar to me, so thanks! Unfortunately I won't know what the variables are in my application, so Reduce isn't so great for that application. $\endgroup$
– Chris K
Oct 14, 2016 at 2:14

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