# Equivalence problem

1. Mar 3, 2009

### soopo

1. The problem statement, all variables and given/known data
Are the statements A and B equivalent with each other?

A. Suppose that n is an integer which is not a perfect square.
B. If n >= 1, then $$\sqrt{n}$$ is either an integer or is irrational.

3. The attempt at a solution
I am keen on saying that the two statements are not equivalent.
However, Oxford's undergraduate booklet claims that they are equivalent.

In my opinion, A is inclined to that n is not a perfect square, while B is neutral.

2. Mar 3, 2009

### praharmitra

they are quite different. Statement 1, is an assumption (which we are assuming to be true), whereas statement 2 is a...well its a statement (that may be true/false)

Also, consider the second statement

It says sqrt(n) is either integer or irrational. This means sqrt(n) could be sqrt(2/3) which is also irrational. However, it is not equivalent to saying n is an "integer" and not a perfect square..

edit: ok, Statement 2 also says n>=1(missed that) so just do the entire same argument for sqrt(3/2), that'll also hold

3. Mar 3, 2009

### praharmitra

they are quite different. Statement 1, is an assumption (which we are assuming to be true), whereas statement 2 is a...well its a statement (that may be true/false)

Also, consider the second statement

It says sqrt(n) is either integer or irrational. This means sqrt(n) could be sqrt(2/3) which is also irrational. However, it is not equivalent to saying n is an "integer" and not a perfect square..

4. Mar 3, 2009

### soopo

I agree with you.

5. Mar 3, 2009

### soopo

Do you mean that the two statements are equivalent?

6. Mar 3, 2009

### dperkin2

No he still means they are not equivalent. Just plug in 3/2 instead of 2/3 in his previous argument of why they are not equivalent.

7. Mar 3, 2009

### soopo

Thank you both!
The problem is now clear.