13.1 - Definition of Groups
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Practice Questions
Test your understanding with targeted questions
What is the definition of a group?
💡 Hint: Remember the four key properties.
Can a set of non-negative integers form a group under addition?
💡 Hint: Consider what happens when you try to find the inverse of an element.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines a group in mathematics?
💡 Hint: Think about the requirements needed for a group.
Is the identity element unique in a group?
💡 Hint: Consider the definition of identity in groups.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Consider the set of rational numbers under addition. Does it form a group? Justify your answer using the group axioms.
💡 Hint: Check each axiom systematically.
Propose a new operation on a set of your choice and prove whether or not it forms a group.
💡 Hint: Define your operation clearly and work through examples.
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