55 798
Assignments Done
97,2%
Successfully Done
In December 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Answer on Real Analysis Question for junel

Question #3881
If a < x < b and a < y < b,& show that |x-y|< b-a. Interpret this geometrically.
Expert's answer
Assume x<y. Then we have a<x<y<b. Then
|x-y|=-(x-y)=y-x=b-x+(y-b)<(b-x), because y<b and thus (y-b)<0. Then
|x-y|>b-x=b-a+(a-x)<(b-a), because a<x and thus (a-x)>0.
So we have got |x-y|<(b-a) for the case when x<y.
In the case when x≥y we can just notice that |x-y|=|y-x| and we can get the same situation as in the previous case. So |x-y|=|y-x|<b-a just like in case 1.
So we’ve proved that if a<x<b and a<y<b then |x-y|<(b-a).
What does it mean geometrically? |x-y| is the distance between points x and y. At the same time (b-a) is the distance between points b and a. As you can see the distance between points x and y must be less than the distance between a and b, becausex and y are inside the section between a and b. Look at the picture bellow:

<img src="../../..//assignments/uploaded_files/static/f0/c8/f0c8ccfc4b5f0019ba2dd1697882fffb.bmp" title="" alt="">

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question