Mathematics Stack Exchange Q A for people studying math at any level and professionals in related fields
(Un-)Countable union of open sets - Mathematics Stack Exchange A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
Prove that that $U (n)$ is an abelian group. Prove that that $U (n)$, which is the set of all numbers relatively prime to $n$ that are greater than or equal to one or less than or equal to $n-1$ is an Abelian
Prove that the sequence (1+1 n)^n is convergent [duplicate] I know the proof using binomial expansion and then by monotone convergence theorem But i want to collect some other proofs without using the binomial expansion *if you could provide the answer w