Real Number Subtracted from Itself leaves Zero

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Theorem

Let $x \in \R$ be a real number.

Then:

$x - x = 0$

where $x - x$ denotes the operation of real subtraction.


Proof

\(\ds x - x\) \(=\) \(\ds x + \paren {-x}\) Definition of Real Subtraction
\(\ds \) \(=\) \(\ds 0\) Inverse for Real Addition

$\blacksquare$


Sources