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Proposition: Addition of Integers Is Cancellative

The addition of integers is cancellative, i.e. for all integers \(x,y,z\in\mathbb Z\), the following laws (both) are fulfilled:

• Left cancellation property: If the equation \(z + x=z + y\) holds, then it implies \(x=y\).

• Right cancellation property: If the equation \(x + z=y + z\) holds, then it implies \(x=y\).

Conversely, the equation \(x=y\) implies

• \(x+z=y+z\) and
• \(z + x=z + y\)

for all \(x,y,z\in\mathbb Z\).

Table of Contents

Proofs: 1

1. Proposition: Contraposition of Cancellative Law for Adding Integers

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Proofs: 1 2

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References

Bibliography

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