- #1

Melodia

- 18

- 0

## Homework Statement

Hello thanks for everyone who helped me on the previous implication proof, here's another problem I'm stuck on:

(Prove or disprove)

## Homework Equations

## The Attempt at a Solution

I think it has something to do with x^2 - y^2 = (x + y)(x - y), and here's my interpretation of "i)":

For every natural x and positive natural e, there exists one or more positive natural sigma so that if |x - y| is smaller than sigma then |x^2 - y^2| must be smaller than e, which works for any natural y.

But I'm lost at where to go next, since sigma could be any number, and with the absolute sign there won't be negative numbers. The same thing with "ii)" and "iii)", where "ii)" simply switched the ordering of the sets and "iii)" limits x and y to 1 and 2.

Thanks for any help!