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Proposition: Distributivity Law For Real Numbers

For arbitrary real numbers \(x,y,z\in\mathbb R\) with the binary operations addition “\( + \)” and multiplication “\(\cdot\)”, the following distributivity laws hold:

\[\begin{array}{ccl}
x\cdot(y+z)&=&(x\cdot y)+(x\cdot z),\quad\quad\text{“left-distributivity property”}\\
(y+z)\cdot x&=&(y\cdot x)+(z\cdot x).\quad\quad\text{“right-distributivity property”}
\end{array}\]

| | | | | created: 2014-03-11 16:39:45 | modified: 2016-01-01 10:07:48 | by: bookofproofs | references: [581], [696]

1.Proof: (related to "Distributivity Law For Real Numbers")

2.Corollary: \(0x=0\)


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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983

[696] Kramer Jürg, von Pippich, Anna-Maria: “Von den natürlichen Zahlen zu den Quaternionen”, Springer-Spektrum, 2013

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