4 ms·
Not just very hard, but actually impossible for almost all transcendentals. Reason being, any description must be finite in length; descriptions therefore form
by colanderman 5y ago
Not just very hard, but actually impossible for almost all transcendentals. Reason being, any description must be finite in length; descriptions therefore form a countable set; but transcendentals are uncountable. The subset of reals which are describable are known as "definable real numbers" [1]. (Notably, all algebraic numbers -- the reals of which form the complement of transcendentals -- are definable by definition.)
[1] https://en.wikipedia.org/wiki/Definable_real_number https://en.wikipedia.org/wiki/Definable_real_number
- lisper 5y agoYes, that's true. But what I intended to convey was that it's very hard in the sense that we have only described a few dozen classes of transcendentals. So the actual limiting factor has to be something other than this counting argument. The hard part is finding descriptions of transcendentals within the space of describable numbers.