13.3.4 - Non-zero Integers under Multiplication
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Practice Questions
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Define a group in abstract algebra.
💡 Hint: Think of things that need to be satisfied for a set to be considered a group.
What is the identity element for multiplication?
💡 Hint: It's the number that doesn't change other numbers when multiplied.
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Interactive Quizzes
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What property fails for non-zero integers under multiplication?
💡 Hint: Think about what happens when you try to find the inverses of integers.
The multiplication of two non-zero integers results in a:
💡 Hint: Recall the definition of closure.
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Challenge Problems
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Demonstrate whether the set of rational numbers under multiplication forms a group. Describe which properties hold and which do not.
💡 Hint: Consider testing each of the four properties explicitly.
Explore how the operation of addition affects the structure of the set of integers and explain why it qualifies them as a group.
💡 Hint: Provide examples for each property.
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