Definition: Subtraction of Integers

The subtraction of integers, written \(x-y\), is defined as the addition of the first integer \(x\) with the inverse of the second integer with respect to addition \((-y)\), formally \[x-y=[a,b]-[c,d]:=[a,b]+[d,c]=[a+d,b+c]=x+(-y).\]

Algorithms: 1 2 3
Definitions: 4 5
Proofs: 6 7 8 9
Propositions: 10


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References

Bibliography

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