# Thread: ~x<x

1. ## ~x<x

I was trying to prove;

$\forall x[\neg (x for all real Nos

But it seems difficult

Is it realy difficult??

2. ## Re: ~x<x

Originally Posted by psolaki
I was trying to prove;

$\forall x[\neg (x for all real Nos

But it seems difficult

Is it realy difficult??
\begin{align*} &\forall x \in \mathbb{R}~~(x=x)=TRUE \Rightarrow \\ &(x < x) = FALSE \Rightarrow \\ &\neg(x<x) = TRUE\end{align*}

maybe I'm naively missing something but the equality relation is reflexive for real numbers.