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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] (current)
nikolaj
Line 2: Line 2:
 ==== Set ==== ==== Set ====
 | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb N,+,\cdot \rangle$ | | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb N,+,\cdot \rangle$ |
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 | $ m=S(k) $ | | $ m=S(k) $ |
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 | @#55EE55: postulate ​  | @#55EE55: $n + 0 = n$ | | @#55EE55: postulate ​  | @#55EE55: $n + 0 = n$ |
 | @#55EE55: postulate ​  | @#55EE55: $n + m = S(n) + k$ | | @#55EE55: postulate ​  | @#55EE55: $n + m = S(n) + k$ |
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 | @#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 ===
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