- #1
ak123456
- 50
- 0
Homework Statement
Let A [tex]\in[/tex]R be a non-empty,bounded set .Define
B=A+1=[tex]\left\{[/tex]a+1:a[tex]\in[/tex]A[tex]\right\}[/tex] Prove that sup(B) =sup(A)+1
Homework Equations
The Attempt at a Solution
let a[tex]\in[/tex]A b[tex]\in[/tex]B s[tex]\in[/tex]R because B=A+1=[tex]\left\{[/tex]a+1:a[tex]\in[/tex]A[tex]\right\}[/tex]
so b=a+1 [tex]\forall[/tex]b[tex]\in[/tex]B s>= b [tex]\rightarrow[/tex] s>=a+1 , s>=a so sup(B) =sup(A)+1
i thought that is too simple in my way , any other ways?