# Analysis math homework

1. Oct 31, 2009

### ak123456

1. The problem statement, all variables and given/known data
Let A $$\in$$R be a non-empty,bounded set .Define
B=A+1=$$\left\{$$a+1:a$$\in$$A$$\right\}$$ Prove that sup(B) =sup(A)+1
2. Relevant equations
3. The attempt at a solution
let a$$\in$$A b$$\in$$B s$$\in$$R because B=A+1=$$\left\{$$a+1:a$$\in$$A$$\right\}$$
so b=a+1 $$\forall$$b$$\in$$B s>= b $$\rightarrow$$ s>=a+1 , s>=a so sup(B) =sup(A)+1
i thought that is too simple in my way , any other ways?

2. Oct 31, 2009

### jgens

Re: analysis

From the definition of $A$ and $B$, if $\mathrm{sup}(A) = \alpha$ then we clearly have that $\alpha + 1 \geq a + 1 = b$. This proves that $\mathrm{sup}(A) + 1$ is an upperbound for $B$. Now can you prove that this number must be the least upper bound?

3. Oct 31, 2009

Re: analysis

i see ,thx