Proposition: Distributivity Law For Natural Numbers

For arbitrary natural numbers \(n,m,p\in\mathbb N\) with the binary operations addition "\( + \)" and multiplication "\(\cdot\)", the following distributivity laws hold:

\[\begin{array}{ccl} (n+m)\cdot p&=&(n\cdot p)+(m\cdot p)\quad\quad\text{"right-distributivity property"},\\ p\cdot(n+m)&=&(p\cdot n)+(p\cdot m).\quad\quad\text{"left-distributivity property"}\\ \end{array}\]

Proofs: 1

Proofs: 1 2 3 4 5 6


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References

Bibliography

  1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013