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 arithmetic_structure_of_integers [2013/09/03 00:24]nikolaj arithmetic_structure_of_integers [2014/03/21 11:11] (current) Both sides previous revision Previous revision 2013/09/03 00:25 nikolaj 2013/09/03 00:24 nikolaj 2013/09/03 00:08 nikolaj 2013/09/03 00:08 nikolaj 2013/09/03 00:06 nikolaj 2013/09/03 00:05 nikolaj created Next revision Previous revision 2013/09/03 00:25 nikolaj 2013/09/03 00:24 nikolaj 2013/09/03 00:08 nikolaj 2013/09/03 00:08 nikolaj 2013/09/03 00:06 nikolaj 2013/09/03 00:05 nikolaj created Line 1: Line 1: ===== 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]]. Line 12: Line 12: === 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]]