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sav08:axioms_for_equality [2008/04/02 00:47] vkuncak |
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| This construction is an algebraic approach to construct from natural numbers one well-known structure. Which one? ++| $({\cal Z}, + , -)$ where ${\cal Z}$ is the set of integers. ++ | This construction is an algebraic approach to construct from natural numbers one well-known structure. Which one? ++| $({\cal Z}, + , -)$ where ${\cal Z}$ is the set of integers. ++ | ||
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| + | Note: this construction can be applied whenever we have an associative and commutative operation $*$ satisfying the cancelation law $x * z = y * z \rightarrow x=y$. It allows us to contruct a structure where operation $*$ has an inverse. What do we obtain if we apply this consutrction to multiplication of strictly positive integers? | ||
| ===== References ===== | ===== References ===== | ||
| * [[Calculus of Computation Textbook]], Section 3.1 | * [[Calculus of Computation Textbook]], Section 3.1 | ||