Real Number Subtracted from Itself leaves Zero
Jump to navigation
Jump to search
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
- 1957: Tom M. Apostol: Mathematical Analysis ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: $\text{1-2}$ Arithmetical properties of real numbers: Axiom $4$