I think you'll need stronger arguments than that
Keep this in mind; generally, if you can't prove something to be
impossible, then it's
always a possibility that it might be the 'truth'. Although the mathematical chances are usually ridiculously tiny, they're still possibilities. Eg, does Astrology work? Does the alignment of stars actually affect the events that occur in the universe? You're probably thinking of course not, but you can't really prove it's impossible; to eliminate ALL uncertainty you'd need to observe this concept for an infinite amount of time.
Some people believe that numbers do exist, that they're actual objects. But they're abstract objects. Numbers exist outside space and time. It might be possible that they exist in another dimension that we can't see. One theory on why gravity is so weak suggests that gravitons exist in another dimension. Just because they're objects that you can't physically touch doesn't mean they don't exist. In this example, when I say 'exist', I mean the same way that a table or chair 'exists.'
Another example is the belief that numbers just describe things that exist. When we count, we count with respect to objects, eg, here's one pencil, and another, now you've got two pencils. But what happens when you run into complex numbers? ie, square root of negative numbers. How would you understand a number such as pi, which never terminates?