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What is the defining characteristic of a sequence compared to a set?
What is the defining characteristic of a sequence compared to a set?
- Repetitions are not allowed and order matters
- Repetitions are not allowed and order does not matter
- Repetitions are allowed and order does not matter
- Repetitions are allowed and order matters (correct)
How can a sequence be formally defined?
How can a sequence be formally defined?
- As a function from natural numbers to the positions of elements
- As a function from positions of elements to natural numbers
- As a function from elements to natural numbers
- As a function from natural numbers to the elements at each position (correct)
What distinguishes a sequence from an indexed family?
What distinguishes a sequence from an indexed family?
- A sequence contains members, while an indexed family contains elements
- A sequence is a function from natural numbers to the elements at each position, while an indexed family is a function from an arbitrary index set (correct)
- A sequence can be finite or infinite, while an indexed family is always infinite
- A sequence allows repetitions, while an indexed family does not
Which of the following examples illustrates a valid sequence?
Which of the following examples illustrates a valid sequence?
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In a sequence, can the same elements appear multiple times at different positions?
In a sequence, can the same elements appear multiple times at different positions?
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