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arithmetic_structure_of_natural_numbers [2014/04/01 14:17] nikolaj |
arithmetic_structure_of_natural_numbers [2014/04/01 14:18] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb N,+,\cdot \rangle$ | | | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb N,+,\cdot \rangle$ | | ||
| - | |||
| | $ m=S(k) $ | | | $ m=S(k) $ | | ||
| - | |||
| | @#55EE55: postulate | @#55EE55: $n + 0 = n$ | | | @#55EE55: postulate | @#55EE55: $n + 0 = n$ | | ||
| | @#55EE55: postulate | @#55EE55: $n + m = S(n) + k$ | | | @#55EE55: postulate | @#55EE55: $n + m = S(n) + k$ | | ||
| - | |||
| | @#55EE55: postulate | @#55EE55: $n \cdot 0 = 0$ | | | @#55EE55: postulate | @#55EE55: $n \cdot 0 = 0$ | | ||
| | @#55EE55: postulate | @#55EE55: $n \cdot m = n + (n \cdot k) $ | | | @#55EE55: postulate | @#55EE55: $n \cdot m = n + (n \cdot k) $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| + | >todo: rewrite the defintion in my current notation | ||
| + | |||
| We'll often omit the multiplication sign. | We'll often omit the multiplication sign. | ||
| === Reference === | === Reference === | ||
| Line 17: | Line 16: | ||
| ==== Parents ==== | ==== Parents ==== | ||
| === Context === | === Context === | ||
| - | [[Successor set]], [[Natural number]] | + | [[Successor set]] |
| + | === Requirements === | ||
| + | [[Natural number]] | ||
| === Element of === | === Element of === | ||
| [[Commutative semiring]] | [[Commutative semiring]] | ||
| === Related === | === Related === | ||
| [[Cardinal arithmetic with types]] | [[Cardinal arithmetic with types]] | ||
