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

Can someone check this for me?

Problem: determine which, if any of the sets if open? closed? compact?

R=reals; Q=rationals and Z=integers.

A= [0,1) U (1,2) is NEITHER

B=Z is CLOSED

C=(.5,1) U (.25,.5) U (.125, 25) U... is OPEN

D={r*sqrt(2) such that r is an element of Q} is NEITHER

E=R-Z is OPEN

2. Relevant equations

How do you find the set of accumuluation points for each of the above sets?

3. The attempt at a solution

my reasoning:

A) the union is [0,1) -1. And [0,1) is neither open nor closed and 1 is bounded. so A is neither.

B) closed by definition?

C) union of open intervals is open

D) Q is not closed and the complement of Q is neither (none of the points in Q are interior points so Q is not open and its complement R-Q has the same property so it is not open, therefore, Q is not closed)

E) from (B), R-Z is the complement of Z, so it is open.

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

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: Open/closed/compact sets

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