# Phi physics help

1. Jul 14, 2008

$$\foralln\inN\varphi(n)/mid/n$$

2. Jul 14, 2008

Re: Phi

i made a mistake in writing

3. Jul 14, 2008

### CRGreathouse

Re: Phi

I imagine you meant
$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$ (which is false; $\varphi(3)\!\not\,\,\mid3$)
but I'm not sure what the question is.

4. Jul 14, 2008

Re: Phi

how we prove
$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$

Last edited by a moderator: Jul 15, 2008
5. Jul 14, 2008

Re: Phi

How we prove that?
\forall n\in\mathbb{N}\;\varphi(n)\mid n

6. Jul 14, 2008

Re: Phi

how we prove the statement in post 3

7. Jul 15, 2008

### CRGreathouse

Re: Phi

$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$

You can't, it's false. It only holds for 1, 2, 4, 6, 8, 12, 16, ... = A007694.

8. Jul 15, 2008

### roam

Re: Phi

Why can’t we derive a contradiction in order to show that it’s false?

9. Jul 15, 2008

### CRGreathouse

Re: Phi

I gave a contradiction, 3, in my first post.

10. Jul 16, 2008

### HallsofIvy

Staff Emeritus
Re: Phi

CRGreathouse, he asked how you prove the contradiction you gave in post 3 and you answered "You can't, it's false. "! You were, of course, referring to his original post, not the post you quoted.

roam, you prove the contradiction by doing the arithmetic. What is $\phi(3)$?

11. Jul 16, 2008

### CRGreathouse

Re: Phi

Ah. I took that to mean 'How do we prove the statement "$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$" from post #3', rather than 'How do we prove the statement "$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$ [...] is false" from post #3'. To me, "$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$" was the only mathematical statement in post #3; "(which is false[...])" is a nonrestrictive clause. '"$$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$" is false' would have been a mathematical statement, but one I only implied. That's why I was so confused by post #6.

Of course a contradiction is an easy way to show that $$\forall n\in\mathbb{N}\;\varphi(n)\mid n$$ fails.