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2 cards from this section. Quick, good the night before a test.
What is a group in abstract algebra?
Think about the properties that define a group.
Identify the identity element for addition in integers.
Consider what number you can add without changing the value.
What is the requirement for a set to be a group?
Reflect on what properties are essential for forming a group.
True or False: Addition modulo k is not a valid group operation.
Look back to how addition modulo k is defined.
Create a new example set and operation, showing if it satisfies the four properties of groups.
Use the defined properties for each check.
Discuss how arching inverses work in negative and positive integers under addition.
Think about how inverses are defined relative to the identity.
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