Question

define countable set and prove countable union is countable sets is countable​

Answer 1

Answer:

Theorem: Every countable union ofcountable sets is countable. We begin byproving a lemma; Lemma 1. A set X iscountable if and only if there exists a surjection f : N → X. ... X is countable if and only if it is finite or denumerable. If X is denumerable, there is a bijection f : N → X.

Answer 2

Step-by-step explanation:

Theorem: Every countable union of countable sets is countable. We begin by proving a lemma; Lemma 1. A set X is countable if and only if there exists a surjection f : N → X. ... X is countable if and only if it is finite or denumerable. If X is denumerable, there is a bijection f : N → X.