A problem on infimum and supremum. Prove.

[Kinetica]

The problem is attached. So is the solution by contradiction.
I would love to hear your feedback if my sol. by contradiction is sufficient enough. Thanks a lot.

 

[lanedance]

so what are you trying to prove?

also i find you'll generally get a quicker response if you type or use tex, that way people can cut and paste and its easy to read...