Hi,

the whole problem and solution is at: Solutions – Baby Rudin – 1.5 (work in progress) « DaFeda's Blog. I'm sorry for posting an external link, just trying to avoid writing it all again. However, I do not think you even need to go there to answer my question.

In my proof I write;

If $\displaystyle \alpha > \beta$ then $\displaystyle -inf(A) > sup(-A)$. Since $\displaystyle sup(-A)\geq -x$ for all $\displaystyle x\in A$ this would imply that

$\displaystyle -inf(A) > -x$ , which is a contradiction since $\displaystyle -inf(A) \geq -x$ for all $\displaystyle x\in A$.

Can I use $\displaystyle \geq$ and $\displaystyle >$ in such a way? I have three different solutions available to me from different people, so I am not looking for another way of solving this.

Hope someone has the time to take a look! Thanks.