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- Not every pair of elements has a difference in
**N**:- ~
**exists**`x`: 0=`x`+1. `x`-`y`:=**such**`z`:`x`=`z`+`y`.- 0-1 is undefined.

- ~
- Introduce a set
**Z**of*integer numbers*such that**N**can be "embedded" into**Z**, and- for all integers
`a`and`b`there is an integer`x`with`a`=`x`+`b`(and consequently`a`-`b`is defined).

*Set-theoretic construction on top of N*.

Author: Wolfgang Schreiner

Last Modification: November 16, 1999