(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A = {ln(1 + q^2) : q is rational}. One needs to find Cl(A) in R with its euclidean topology.

3. The attempt at a solution

So, the set A is a countable subset of [0, +∞>. The closure is, by definition, the intersection of all closed sets containing A. So, Cl(A) would be [0, +∞> itself , right?

I'm just curious about my solution, thanks in advance.

By the way, another way to look at it would be the fact that A is dense in [0, +∞> (since every open interval in [0, +∞> intersects A), so Cl(A) = [0, +∞>. I'm not really sure about this, although it seems quite obvious. Can we, for every <a, b> in [0, +∞>, find some rational q such that ln(1 + q^2) is contained in <a, b>?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Closure of a countable subset of the reals

**Physics Forums | Science Articles, Homework Help, Discussion**