- #1
llursweetiell
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Homework Statement
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
Homework Equations
How do you find the set of accumuluation points for each of the above sets?
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.