The opposite of Qiaochu's dictum is just as misleading - "formulas are functions". There are a lot of non-denoting expressions! It's just that mathematicians don't tend to write non-denoting terms very often. Of course, there's a good reason for that - you can't prove anything interesting about non-denoting terms (or rather, way too much). But then students never get the intuition that there are expressions which are 'junk', nor tools to prove that something is 'junk'.

My favourite 'junk' expression is $$1/\frac{1}{\left( x - x \right) } $$

Lest you think this is not very important, try to "teach" first-year calculus to a computer, and you'll see how these non-denoting terms are most troublesome.