Right, but to be clear, it's not that ultrafinitists like Wildberger believe that they can express all the real numbers; rather, they believe that those inexpressible real numbers don't actually exist.
E.g. when you calculate the area of a plot of land do you take into account the curvature of the Earth? You have to make a bunch of compromises in the first place to even talk about what the area of a plot land means.
Math is a bunch of useful systems that we humans have devised. We tend to gravitate towards the ones that help us describe and predict things in the real world.
But there is plenty of math which doesn't do either. It's just as real as the math that does.
https://plato.stanford.edu/entries/church-turing/decision-pr...
The short answer is that they deal with such things symbolically.