Oh, you're right. For that I would need to explicit the construction of the sequence n0, n1, … but that's impossible : if I can find such sequence, my proof holds but at the same time such sequence shows that the set is countable => contradiction, hence there is no such sequence.
But well, now that we've proven that such sequence doesn't exist, we've proven that the given set is not countable !
Not the most elegant proof ever, but I think it works.
Actually it doesn't: what if the given sequence exists but cannot be expressed with words ? (This is exactly the same thing than «a real number that can't ne expressed with words» which is what I'm trying to demonstrate not to exist. I'm going nowhere)
But well, now that we've proven that such sequence doesn't exist, we've proven that the given set is not countable !
Not the most elegant proof ever, but I think it works.