let inf S=m and sup S=M.

if T={|x-y| :x,y belong to S},

then prove that sup T= M-m

Printable View

- January 13th 2011, 11:32 AMluckylawrancesupremum
let inf S=m and sup S=M.

if T={|x-y| :x,y belong to S},

then prove that sup T= M-m - January 13th 2011, 12:16 PMDrexel28
- January 13th 2011, 12:20 PMCSM
Intuitively the difference between to elements in S is the biggest when one is the biggest element while the other one is the smallest (or vice versa).

- January 14th 2011, 04:30 AMluckylawrance
Respected, the idea i have is that difference between two numbers is greatest when one is largest and other is smallest in S. but i don't know how to write the proof in proper way.

- January 15th 2011, 03:54 PMDrexel28