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
Proof that $U (n)$ is connected - Mathematics Stack Exchange Thanks for the link @muzzlator I've just had a look at it and it's very interesting (and seems a lot simpler), however it uses methods a little different to those that I have been using for the course I am studying
How do we calculate factorials for numbers with decimal places? I was playing with my calculator when I tried $1 5!$ It came out to be $1 32934038817$ Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\\times1$, but how do we e