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Math Help - ~x<x

  1. #1
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    ~x<x

    I was trying to prove;

    \forall x[\neg (x<x)] for all real Nos

    But it seems difficult

    Is it realy difficult??
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  2. #2
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    Re: ~x<x

    Quote Originally Posted by psolaki View Post
    I was trying to prove;

    \forall x[\neg (x<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.
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