22.3.2.1 - Proof by Contradiction
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Practice Questions
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What does the characteristic of a field represent?
💡 Hint: Think about addition and returning to zero.
Define what a prime number is.
💡 Hint: Consider how many factors it has.
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Interactive Quizzes
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What denotes the characteristic of a field?
💡 Hint: Think of how elements interact in addition.
True or False: The characteristic of any finite field must be a prime number.
💡 Hint: Recall the definitions and the implications of composite numbers.
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Challenge Problems
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Find the characteristic of the finite field containing the elements {0, 1, 2} with operations defined by addition and multiplication modulo 3.
💡 Hint: Focus on how the operations cycle through the elements.
If we assume a field has a characteristic of 6, demonstrate how you would derive a contradiction.
💡 Hint: Break the assumption into cases for each factor of 6.
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