Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
arithmetic_structure_of_natural_numbers [2014/04/01 14:17] nikolaj |
arithmetic_structure_of_natural_numbers [2014/04/01 14:18] nikolaj |
||
|---|---|---|---|
| Line 2: | Line 2: | ||
| ==== 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 === | ||
