jsbgir

The set of transcendental but computable numbers is also countable, however: there is a countable number of algorithms. Therefore, the majority of the reals are uncomputable, like Chaintin's constant (the probability that a random algorithm halts). This can in turn be made stronger by noticing that the definition of Chaitin's constant is finite, and by the same argument, definable real numbers are countable. It follows that the majority of the reals are indefinable.

I can't recommend the Pimsleur language courses enough. They teach languages in a way that's similar to how a toddler learns to speak - by going from sounds to words, and by gradually expanding your lexicon while jogging your memory on previously learned words and phrases. In my experience, 45-50 daily 30-minute lessons were enough to comfortably navigate a new country. Most courses include ninety 30-minute lessons.

> For example, if you want to delete 3 words, there is an action to delete (d) and a motion to move forward one word (w): 3dw (read (3) times, (d)elete (w)ord)

I prefer to use d3w since it feels more like English. It's also more compatible with other combinations like ci" ('change inside quotes', e.g. to change a string), ca" ('change around quotes', e.g. to replace a string with a constant), or yt{ ('yank to brace').

This is really interesting. We could take it further and say that, given that some uncomputable reals have a finite definition (e.g. "the probability that a random algorithm halts"), there is a countable number of definable reals (by assigning a Godel number to each definition), so the uncountability of the reals is strictly due to indefinable numbers!