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arithmetic_structure_of_integers [2013/09/03 00:24] nikolaj |
arithmetic_structure_of_integers [2014/03/21 11:11] (current) |
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===== Arithmetic structure of integers ===== | ===== Arithmetic structure of integers ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#FFBB00: $\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb Z,+_\mathbb{Z},\cdot_\mathbb{Z} \rangle$ | |
- | | @#55EE55: $[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ | | + | | @#55EE55: postulate | @#55EE55: $[\langle a,b\rangle]+_\mathbb{Z}[\langle m,n\rangle]=[\langle a+m,b+n\rangle]$ | |
- | | @#55EE55: $[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\cdot m+b\cdot n,a\cdot n+b\cdot m\rangle]$ | | + | | @#55EE55: postulate | @#55EE55: $[\langle a,b\rangle]\cdot_\mathbb{Z}[\langle m,n\rangle]=[\langle a\ m+b\ n,a\ n+b\ m\rangle]$ | |
The operations $+$ and $\cdot$ on the right hand sides are these of [[arithmetic structure of natural numbers]]. | The operations $+$ and $\cdot$ on the right hand sides are these of [[arithmetic structure of natural numbers]]. | ||
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=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Integer|Integer]] | Wikipedia: [[http://en.wikipedia.org/wiki/Integer|Integer]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
- | === Requirements === | + | === Context === |
[[Integer]] | [[Integer]] | ||
=== Element of === | === Element of === | ||
[[Unital ring]] | [[Unital ring]] |