57 365
Assignments Done
Successfully Done
In February 2018
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 Shiro

Question #4227
Show that a set of real numbers E is bounded if and only if there is a positive number r so that absolute value x<r for all x in e.
Expert's answer
A set S of real numbers is called bounded from above if there is a real number k such that k ≥ s for all s in S. The number k is called an upper
bound of S.A set of real numbers is bounded from below if there is a real number
m such that s>=m fo all s in S. m is lower bound .
A set S is bounded if it has both upper and lower bounds.
1. =>
set S is bounded=> it has lower and upper bounds, respectively m and k. m=>k
if m,k>0 then we take r=m and |x|<r for all x in S (cause in this case x>0 and |x|=x)
if m>0, k<0 then we take r=max{m, |k|}
if m,k<0 r=|k|
assume |x|<r for all x in S
Hence -r<x<r for all x
so x>-r bounded from below
x<r bounded from above

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!


No comments. Be first!

Leave a comment

Ask Your question