my menu should float left, it is not alone in the menu bar
I believe your mistake is actually your false premise. You don't need to float the elements to keep them inline. If your point is keeping the p and the ul side-by-side, change their display property.
Floating will remove the ability of centering the elements, but display: inline-block for example, lets you horizontally align the elements by their parent, with text-align: center:
font-family: helvetica, sans-serif;
margin: 10px auto 0 auto;
border: 1px solid black;
i am surprised by the number of questions i see that say "i floated my element left, but now i can't center it!".