| 1. | Transitivity however, depends on the definition of the set of elementary operations.
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| 2. | What is important is that each elementary operation has a constant cost.
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| 3. | Is not in closed form because the summation entails an infinite number of elementary operations.
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| 4. | The generator matrices of equivalent codes can be obtained from one another via the following elementary operations:
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| 5. | Computer processors have well-defined elementary operations.
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| 6. | Hence the universe of sets under ZFC is not closed under the elementary operations of the algebra of sets.
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| 7. | Alternatively, a sequence of elementary operations that reduces a single row may be viewed as multiplication by a Frobenius matrix.
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| 8. | A set of elementary operations which will be used in the algorithm is chosen and their costs are arbitrarily set to 1.
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| 9. | Early programs had to be painstakingly crafted using the instructions ( elementary operations ) of the particular machine, often in binary notation.
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| 10. | Thus, the amount of time taken and the number of elementary operations performed by the algorithm differ by at most a constant factor.
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