I think it depends on what you mean by false. I've always thought of falsity as a continuum. At one end are obvious non sequiturs like 1=3. A little further along are the novice blunders everybody makes while learning the theory. At the far end are propositions where you have to cook up a really abstruse counterexample to show they aren't true. But that's tantamount to saying that they almost are true. And in fact a lot of the time you can treat them as true and not get into trouble.

Physicists, to take a notorious example, spend a lot more time on the real line than mathematicians do, but in their day to day work they ignore most of what we know about the real number system.