Please help me in understanding the difference between theorems 2.12 & 2.14 of Rudin's Principles of Mathematical Analysis. Both are sets of sequences. Set S in Th.2.12 is union of countable sequences While set A in Th 2.14 is set of "all" sequences. Is set A uncountable only because it has "all" sequences, whereas set A is countable because it does not have "all" sequences, but only countable sequences? Thanks in advance.