# Analysis question

1. Apr 19, 2010

### zilla

1. The problem statement, all variables and given/known data

Suppose that each of A and B is a set such that:
(a) A is a subset of [0,1], B is a subset of [0,1]
(b) Neither of A or B is empty
(c) 0 (zero) is an element of A
(d) The union of A & B = [0,1]
(e) A & B are disjoint
(f) A contains no limit points of B.

Then, B contains a limit point of A.

2. Relevant equations
None

3. The attempt at a solution
Not sure where to go with it...

2. Apr 19, 2010

### ystael

If $$A$$ contains no limit point of $$B$$, then what kind of points does $$A$$ consist of? (What must $$A$$ look like near $$0$$? How far from $$0$$ can you "push" this appearance?)