[raverbashing]

Yep, this is a good example. And maybe it helps illustrating my point

On N and Q we can come up with any number we want. Even though there are infinite numbers, we can come up with any number

On R we can do that as well. But at the same time we can come with "vapid" statements like "for each x in R exists x' < x" which are completely correct but don't really mean anything.

True, the R's are a good foundation, and in a way they do exist physically (after all, Pi exists in nature).