Practice Group of Non-zero Real Numbers under Multiplication - 13.3.3 | 13. Group Theory | Discrete Mathematics - Vol 3
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Group of Non-zero Real Numbers under Multiplication

13.3.3 - Group of Non-zero Real Numbers under Multiplication

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

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.

Question 2 Easy

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?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which property guarantees that the product of two elements is still within the set?

Closure
Identity
Inverse

💡 Hint: Think about what happens when you add two elements.

Question 2

True or False: Every integer has a multiplicative inverse within the set of integers.

True
False

💡 Hint: Consider if dividing integers always yields integers.

3 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

Prove that addition of integers is a group.

💡 Hint: Use the definitions of axioms to support your argument.

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