- #1

- 4

- 0

## Homework Statement

Let [a,b] be an interval and let A be a subset of [a,b] and suppose that A is an infinite set.

Suppose that A is uncountable. Prove that there exists a point z which is an element of [a,b] such that A intersect I is uncountable for every open interval I that contains z.

## Homework Equations

I don't really know how to start this problem. I know I can use the fact that a set that contains an uncountable subset is uncountable. Any help would be appreciated

## The Attempt at a Solution

I know z is an element of I, and that I is uncountable. I also know z is an element of [a

_{n}, b

_{n}]. I know there exists a unique point z in [a

_{n}, b

_{n}] and I know A is uncountable.