Talk:Proportion is Symmetric

Surely $\propto$ is symmetric on all of $\R$?? I don't get what's questionable... --GFauxPas (talk) 21:46, 16 September 2014 (UTC)

What's $k^{-1}$ when $k = 0$? --prime mover (talk) 21:49, 16 September 2014 (UTC)

$k \ne 0$ by the definition of proportion --GFauxPas (talk) 21:49, 16 September 2014 (UTC)

Hint: So what happens when either $x$ or $y$ equals $0$? What's $k$ then? --prime mover (talk) 21:53, 16 September 2014 (UTC)

Let $k \neq 0$. So $0 = ky \iff y = 0$, so $0 \propto y \implies y = 0$. likewise $y = k0 \iff y = 0$, so $x \propto 0 \implies x = 0$.

So $0 = k0$ no matter what $k$ is, so any choice of $k$ will yield $0 \propto 0$. Is there some caveat somewhere that $k$ has to be unique? --GFauxPas (talk) 22:03, 16 September 2014 (UTC)

Anyone else? I'm tired. --prime mover (talk) 22:09, 16 September 2014 (UTC)

Okay yes, I get this now ... sorry, I was tired last night and didn't get the point. --prime mover (talk) 06:39, 17 September 2014 (UTC)