If you claim a construction is obvious and dispells confusion, that construction should not have any readings that are obviously wrong. Sure, charitable readin

If you claim a construction is obvious and dispells confusion, that construction should not have any readings that are obviously wrong. Sure, charitable readings of informed readers will find it obvious. But less informed readers, or skeptical readers, will see the wrong interpretation. For a skeptical reader to then think "since they state its obvious, perhaps they refer to the general uncomputability of the reals", is not surprising. Regarding the actual construction, once its well formulated, it becomes a lot less 'natural'. Since the definition is already taking about computable (or representable) reals, it is much less surprising that the result is a non-computable function. The beauty of the example is that the definition of the function never refers to any ideas from computational theory. Hence the article serves as a counter example to the theory "You never get uncomputable functions in fields outside of computational theory".