![SOLVED: One of the following is false: a) The countable union of countable sets is countable. b) Any subset of a countable set is countable. c) Any subset of an uncountable set SOLVED: One of the following is false: a) The countable union of countable sets is countable. b) Any subset of a countable set is countable. c) Any subset of an uncountable set](https://cdn.numerade.com/ask_images/f773babd7a974e65a43e7e4656c2df9c.jpg)
SOLVED: One of the following is false: a) The countable union of countable sets is countable. b) Any subset of a countable set is countable. c) Any subset of an uncountable set
![real analysis - Rudin's Proof for Countable union of Countable Sets are Countable. - Mathematics Stack Exchange real analysis - Rudin's Proof for Countable union of Countable Sets are Countable. - Mathematics Stack Exchange](https://i.stack.imgur.com/z3KAq.png)
real analysis - Rudin's Proof for Countable union of Countable Sets are Countable. - Mathematics Stack Exchange
![elementary set theory - proof that union of a sequence of countable sets is countable. - Mathematics Stack Exchange elementary set theory - proof that union of a sequence of countable sets is countable. - Mathematics Stack Exchange](https://i.stack.imgur.com/CicTG.png)
elementary set theory - proof that union of a sequence of countable sets is countable. - Mathematics Stack Exchange
![real analysis - Walter Rudin's proof: countable union of countable sets is countable - Mathematics Stack Exchange real analysis - Walter Rudin's proof: countable union of countable sets is countable - Mathematics Stack Exchange](https://i.stack.imgur.com/1ltg3.png)
real analysis - Walter Rudin's proof: countable union of countable sets is countable - Mathematics Stack Exchange
![real analysis - The set of discontinuous points is countable union of closed sets - Mathematics Stack Exchange real analysis - The set of discontinuous points is countable union of closed sets - Mathematics Stack Exchange](https://i.stack.imgur.com/oq7gJ.jpg)
real analysis - The set of discontinuous points is countable union of closed sets - Mathematics Stack Exchange
![SOLVED: CHAPTER 11 Countability DEFINITION 11.1. A set A is countable if either A is finite or, in the latter case, A is countably infinite. DEFINITION 11.2. A set A is uncountable SOLVED: CHAPTER 11 Countability DEFINITION 11.1. A set A is countable if either A is finite or, in the latter case, A is countably infinite. DEFINITION 11.2. A set A is uncountable](https://cdn.numerade.com/ask_images/234df48974f3492abaf7b75abd699c9e.jpg)