Needs:
Integer Numbers
Natural Sums
Needed by:
Integer Additive Inverses
Integer Arithmetic
Links:
Sheet PDF
Graph PDF

Integer Sums

Why

We want sums to follow those of natural numbers.1

Definition

Consider [(a,b)],[(c,d)]Z. We define the integer sum of [(a,b)] with [(c,d)] as [(a+c,b+d)].2

Notation

We denote the sum of [(a,b)] and [(c,d)] by [(a,b)]+[(b,c)] So if x,yZ then the sum of x and y is x+y.


  1. Future editions will modify this. ↩︎
  2. One needs to show that this is well-defined. The account will appear in future editions. ↩︎
Copyright © 2023 The Bourbaki Authors — All rights reserved — Version 13a6779cc About Show the old page view