# Why can't a confidence level be 100%?

$- \infty \le n \le \infty$
I had wondered that in the past but then you have to think about what is the normal distribution. We know that it covers values from $- \infty \to \infty$. This means no matter how wide your range is constructed you will never include all the possible numbers. If you look at most tables I think they report something like .999...
Simply put you can never bee 100% certain you captured the true population value because $- \infty \le n \le \infty$ and any bounded interval will clearly not cover all the possible values. I would argue that being 99% confident seems pretty good to me.