Alright, back to computing science then. 
Give simple, naturally occuring examples of the following:
A) A countable infinite set
B) An uncountable infinite set
C) A countable finite set
D) An uncountable finite set

Give simple, naturally occuring examples of the following:
A) A countable infinite set
B) An uncountable infinite set
C) A countable finite set
D) An uncountable finite set