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Write mathematical formula for:

Not every square root of a positive number is positive number (using $*,+,=,1,>,0$)

That is my solution that I am not sure about as I am not really good in these things:

$$\lnot \forall x(\exists k(x*x=k \land k>0) \Rightarrow x>0)$$

What about it?

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    $\begingroup$ I think your formula is misparenthesized (the last occurrence of $x$ should be under the scope of $\forall$), it should be $\lnot\forall x(\exists k(x∗x=k \land k>0) \to x>0)$. $\endgroup$ – Taroccoesbrocco Jan 31 '18 at 10:48
  • $\begingroup$ I think you are right. It should be. $\endgroup$ – James Smith Jan 31 '18 at 10:55
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I would write it in the following way, but yours is correct :)

$$\neg (\forall x\vert x>0\Rightarrow (\forall k\vert k*k=x \Rightarrow k >0))$$

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