(related to Corollary: A product of two real numbers is zero if and only if at least one of these numbers is zero.)
Let \(x,y\) be real numbers.
- Let \(yx=0\), where $0$ denotes the real zero.
- Assume \(y\neq 0\). We have to show that $x=0.$
- Therefore, $x=0$.
- Let at least on of the two numbers \(x,y\) equal zero.
- Then it follows immediately as a corollary from $0x=0$, that \(xy=0.\)
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983