Practice Set Of Real Numbers With Decimal Representation Of Only 1s (9.5)

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9 questions

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6 sample questions

Question 1.
Define Cardinality.
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Think about how many elements a set has.
Question 2.
What is an injective function?
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Remember, no two outputs should be the same for different inputs.
3Question 3.
What does cardinality refer to?
- Size of a set
- Shape of a set
- Color of elements
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Think about how big the set is.
4Question 4.
True or False: An injective function maps two inputs to the same output.
- True
- False
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Recall the definition of injective functions.
Question 5.
Prove that for any set A, removing a finite number of elements will leave the cardinality either unchanged or smaller.
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Consider the implications of finite vs infinite removals.
Question 6.
Show that the union of two countably infinite sets is countably infinite.
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Think about list ordering.

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