# Thread: Is this question ridiculous? (set theory)

1. ## 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.

2. Originally Posted by swtdelicaterose
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