Do Numbers Exist?

One question that I have always pondered is whether numbers exist or not. I’m tempted to think no they don’t. What would it mean for a number to exist? How would a number exist? The number 3 sure looks like a particular, but it also looks like it can be a universal. There can be 3 apples here in my room and 3 bananas in your room. Does that mean they both possess threeness? There is a view called Fictionalism about numbers. This view says numbers are useful fictions that we invent. Thus, strictly speaking, 3 + 3 = 6 is literally false because there are no such things as 3 and 6. This seems like an absurd consequence but I think that Fictionalism can account for this by just reinterpreting “3 + 3 = 6″ as “in the natural system of numbers, 3 + 3 = 6.” This leaves the option open as to whether the natural system of numbers is a fiction or not.