13.3.2 - Non-negative Integers under Addition
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Practice Questions
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Define the closure property in the context of group theory.
💡 Hint: Think about what happens when you add two elements in a set.
What is the identity element for addition?
💡 Hint: Consider the effect of adding zero to a number.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the closure property ensure in a group?
💡 Hint: Think about adding elements and their results.
True or False: Every set that includes zero and is closed under addition is a group.
💡 Hint: Consider the necessity of having inverses in the group definition.
2 more questions available
Challenge Problems
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Given the set of even integers, do they form a group under addition? Justify your answer based on the group properties.
💡 Hint: Check each property to confirm.
Design a new set and operation that fails to meet one of the group properties and identify which property is violated.
💡 Hint: Think about operations that might produce results outside the defined set.
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