- #1
1MileCrash
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Homework Statement
I'll spare most of the details, R = {(x,y) | |x-y| < 5}
I need to find a counter-example to show that it is not transitive. I'm having trouble.
The Attempt at a Solution
First, in order to find a counter example, I know this must be satisfied:
| x - y | < 5
|y - z | < 5
|x - z | >= 5
So to remove the absolute values, I did (which makes sense to me on paper):
-5 < x - y < 5
-5 < y - z < 5
x - z > 5 or x - z <= -5
So to isolate x and y, I did this (which again, only makes sense to me on paper)
-5 + y < x < 5 + y
-5 - y < -z < 5 - y
-5 + y < z < 5 + y
So I have "information" about both z and x, but how can I use that in:
x - z > 5 or x - z <= -5
To make it say something about y? (since that's what I chose to express x and z in terms of)
I feel like I essentially have a system of inequalities:
-5 + y < z < 5 + y
-5 + y < x < 5 + y
x - z > 5 or x - z <= -5
Am I on the right track here? I'm just doing what makes sense to me, I've never dealt with inequalities in any classes in this way.