Mathematical Sequences Quiz
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Questions and Answers

What is the defining feature of a sequence that distinguishes it from a set?

  • Repetitions are not allowed but order matters
  • Repetitions are allowed and order matters (correct)
  • Repetitions are not allowed and order does not matter
  • Repetitions are allowed but order does not matter
  • What is an example of a valid sequence?

  • (3, 6, 9, 12, 15)
  • (1, 1, 2, 3, 5, 8) (correct)
  • (2, 4, 6, 8, 10)
  • (1, 2, 3, 4, 5, 6)
  • How can a sequence be formally defined?

  • As a function from elements to natural numbers
  • As a function from natural numbers to the positions of elements
  • As a set of elements with specific positions
  • As a function from natural numbers to the elements at each position (correct)
  • What is the length of a sequence?

    <p>The number of elements in the sequence</p> Signup and view all the answers

    How does a sequence differ from an indexed family?

    <p>A sequence is a function from natural numbers, while an indexed family is a function from an arbitrary index set</p> Signup and view all the answers

    How can a sequence be defined formally?

    <p>As a function from natural numbers to the elements at each position</p> Signup and view all the answers

    What distinguishes a sequence from a set?

    <p>Order matters in a sequence but not in a set</p> Signup and view all the answers

    What is the defining characteristic of a valid sequence?

    <p>Repetitions of elements at different positions are allowed</p> Signup and view all the answers

    How does an indexed family differ from a sequence?

    <p>An indexed family is defined as a function from an arbitrary index set, while a sequence is defined as a function from natural numbers</p> Signup and view all the answers

    What is a valid example of a sequence?

    <p>(3, 5, 3, 7, 8)</p> Signup and view all the answers

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