Honestly, I haven't a bloody clue, and just out of curiosity, why is it just that but instead of but ?
Sorry, I know I should know this, but I barely scraped by analysis in undergrad :-(
Forget , we can do this for . So ,if were continuous at then we should be able to find some such that , right? But, for example if you claimed to me that you have found a which works I can show you that you're wrong. To see this we know by the Archimedean principle I can find some such that and , right? So, consider then clearly but , and and so the you claimed work didn't, and so you can't find any which works. So, it isn't continuous. Make sense?