> The fact that we can only write down only countably many expressions for numbers doesn't mean that there are numbers that we may never write expressions for
Yes it does: there are countably many numbers we can define, and the reals are uncountable, therefore there are uncountably many numbers that cannot be defined.
Yes it does: there are countably many numbers we can define, and the reals are uncountable, therefore there are uncountably many numbers that cannot be defined.