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I have a statement that I want to express in logic symbols and decide if its true or false. The following is my attempt:

Every real number can be written as a difference of two positive real numbers. $$(\forall x \in \mathbb R)(\exists a,b \in \mathbb R)[(a,b>0) \wedge(x=a-b)]$$ I know this one I definitely didn't get it right. But that was my best attempt.
This statement is True because for positive real numbers, take x to be that number and y to be 0. Then x-0=x. For negative numbers, take x = 0 and y to be that negative number. Then 0-y = -y. For 0, take x = y>0. Then x-y=0.

Thanks in advance.

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    $\begingroup$ $0=42-42$. And some people would say that zero is a natural number, which would derail your first argument. $\endgroup$
    – Gerry Myerson
    Commented Dec 28, 2020 at 1:00

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$(\forall x \in \mathbb{R})(\exists a,b \in \mathbb{R^{+}}) [x=a-b]$

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