Can you? There’s no “first real larger than 2”, for example, so if I define the definable reals as {0, 1, 2}, what is that first real? In general, you also can

Can you? There’s no “first real larger than 2”, for example, so if I define the definable reals as {0, 1, 2}, what is that first real? In general, you also can’t use Cantor’s diagonal argument on the list of definable reals because there are numbers in there that aren’t computable.