## Most recent change of Integer

Edit made on September 25, 2018 by ColinWright at 19:47:54

Deleted text in red / Inserted text in green

WW
WM
The Integers are the whole numbers, both positive and negative and including zero.
The usual symbol for the set of integers is a "blackboard bold" *Z* - a *Z* with two strokes on the diagonal.

The integers have a natural embedding into the rational numbers, and contain the natural numbers.

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!! More technical stuff ...
The integers can be constructed from the counting numbers (the natural numbers
not including 0) as follows:
* Let P be the collection of all pairs of whole numbers:
** EQN:P=\{(a,b):a,b\in{N}}
* Let /(a,b)/ be equivalent to /(c,d)/ if /a+d=b+c./
* For any pair /(a,b)/ we can consider the collection of all pairs equivalent to it.
** This collection is called the equivance class of /(a,b),/ and we write it as /E(a,b)/
* We can now define arithmetic operations on the equivalence classes:
** The sum is obtained as /E(a,b)+E(c,d)/=/E(a+c,b+d)/
** The difference is obtained as /E(a,b)-E(c,d)/=/E(a+d,b+c)/