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2 cards from this section. Quick, good the night before a test.
Identify the identity element for the group of integers under addition.
Think about what number you can add to any integer to get that integer back.
Is the set of positive integers under addition a group? Why or why not?
Consider if you have '0' or a similar number in that set.
What is the identity element of the group of integers under addition?
Look at what happens when you add 0.
True or False: Every group is Abelian.
Think about the order of operations in groups.
Prove that the identity element is unique in any group.
Use the definitions of identity element properties in your proof.
Consider a set of complex numbers under multiplication. Describe the identity element and prove its existence.
Apply the definition of multiplication for complex numbers.
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