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Math Help - Is this question ridiculous? (set theory)

  1. #1
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    Is this question ridiculous? (set theory)

    Suppose that A = {1, 2, 3, . . . , 271}.

    Find the number of sets B in P(Z+) such that A is a subset of B where P(Z+) is the powerset of the set of all positive integers.

    Would this question be infinite? Since Integers are infinite, then the powerset would be infinite. As long as B has elements {1, 2, ... , 271} it can have an infinite amount of any other elements and A would still be a subset of B.

    Thanks for the help.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by swtdelicaterose View Post
    Suppose that A = {1, 2, 3, . . . , 271}.

    Find the number of sets B in P(Z+) such that A is a subset of B where P(Z+) is the powerset of the set of all positive integers.

    Would this question be infinite? Since Integers are infinite, then the powerset would be infinite. As long as B has elements {1, 2, ... , 271} it can have an infinite amount of any other elements and A would still be a subset of B.

    Thanks for the help.
    Are you saying find the cardinality of the class of sets \left\{B\subseteq\mathcal{P}:A\subseteq B\right\}? What do you think?

    Hint:
    Spoiler:


    This set can be written as \mathcal{P}(\mathbb{N})-\mathcal{P}(A)\cup\{A\}, but the former is finite...sooo
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