13.2.3 - Identity Element
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Practice Questions
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Identify the identity element for the group of integers under addition.
💡 Hint: Think about what number you can add to any integer to get that integer back.
Is the set of positive integers under addition a group? Why or why not?
💡 Hint: Consider if you have '0' or a similar number in that set.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the identity element of the group of integers under addition?
💡 Hint: Look at what happens when you add 0.
True or False: Every group is Abelian.
💡 Hint: Think about the order of operations in groups.
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Challenge Problems
Push your limits with advanced challenges
Prove that the identity element is unique in any group.
💡 Hint: Use the definitions of identity element properties in your proof.
Consider a set of complex numbers under multiplication. Describe the identity element and prove its existence.
💡 Hint: Apply the definition of multiplication for complex numbers.
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