You are Here: Home >< Maths

# metric space watch

1. consider R2 (real numbers -2dimensional) with standard euclidean distance
and a subset

A={(x,y): x\=0, y/x belongs to Q (rational numbers) }

i need help finding its closure and interior, i think interior will be empty set, but i'm still not sure how to show both.
2. Think about this geometrically: your set is essentially the set of lines through the origin which have rational gradient, but with the point at the origin removed.

Now, pick any point in and a ball of arbitrary radius about that point. Must it contain some point which lies on a line with rational gradient? So what you can you say about the closure of ?

And also, pick any point in . Can you find some ball around that point which doesn't contain any points which lie on lines of irrational gradient? So what you can you say about the interior of ?
3. Thank you! i understand now.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 20, 2011
The home of Results and Clearing

### 3,094

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams