For more information about countable and uncountable sets, see books about "Analysis" (as advanced calculus is called). For example, Introductory Real Analysis, by A.N. Kolmogorov and S.V. Fomin (see ...
Advanced English learners frequently make recurring grammar errors that impact clarity and precision. Common issues include misuse of articles, incorrect subject-verb agreement, preposition errors, ...
What exactly are countable nouns and how are they different from other nouns? Countable nouns are exactly what you think they are with no exceptions. They are the names of things that you can count.