13.3.3 - Group of Non-zero Real Numbers under Multiplication
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Practice Questions
Test your understanding with targeted questions
What property ensures that the operation between any two elements of a group results in an element within the set?
💡 Hint: Think about the 'closure' of a set.
What is the identity element when using multiplication in a group of non-zero real numbers?
💡 Hint: What number keeps other numbers the same when multiplied?
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Interactive Quizzes
Quick quizzes to reinforce your learning
Which property guarantees that the product of two elements is still within the set?
💡 Hint: Think about what happens when you add two elements.
True or False: Every integer has a multiplicative inverse within the set of integers.
💡 Hint: Consider if dividing integers always yields integers.
3 more questions available
Challenge Problems
Push your limits with advanced challenges
Create a set that fails to meet the group axioms and identify which axiom is violated.
💡 Hint: Explore what happens with the operation on elements of this set.
Prove that addition of integers is a group.
💡 Hint: Use the definitions of axioms to support your argument.
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