Could someone please check my work

Prove : If x 20 and XEE for all Exo, Then X= 0. Suppose for The Sake of Contradiction That X$0. 7 xco or * >o . Case 1: Suppose X20. # X 20 is a contradiction. Thus, it is nor The Case That X*0. Case 2: Suppose X 70. > IT is nor the case That X = E > D VE>O Since X cannot be less than or equal To all positive numbers, including itself. Hence, it is not The case That X$0. In either case, it is not The case that X10. Thus, X= O. Therefore, by contradiction, if x 20 and X = E for all EXO, Then X= 0