Proposition: Addition Of Natural Numbers
For any two natural numbers \(n\) and \(m\), there is exactly one natural number \(n+m\), called the sum of the natural numbers \(n\) and \(m\). The operation "\(+\)" is called the addition of natural numbers and is defined recursively by
\[\begin{array}{ccl}
n+0&:=&n,\\
n+m^+&:=&(n+m)^+,
\end{array}
\]
where \(n^+\) denotes the successor of \(n\).
Table of Contents
Proofs: 1 Corollaries: 1
- Proposition: Addition Of Natural Numbers Is Associative
- Proposition: Addition of Natural Numbers Is Commutative
- Proposition: Addition of Natural Numbers Is Cancellative
- Proposition: Uniqueness of Natural Zero
Mentioned in:
Corollaries: 1
Definitions: 2 3
Examples: 4 5 6
Proofs: 7 8 9 10 11 12 13 14 15 16 17 18 19
Propositions: 20 21 22 23 24 25 26 27 28
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References
Bibliography
- Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013
- Landau, Edmund: "Grundlagen der Analysis", Heldermann Verlag, 2008
