query: Proving that all sets of size n have $2^n$ subsets
positive_passages.docid: 44214
positive_passages.text: The number of subsets of a set of cardinality $n$
negative_passages.docid: 1627
negative_passages.text: Cartesian product of an arbitrary number of sets
negative_passages.docid: 22154
negative_passages.text: Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
negative_passages.docid: 51617
negative_passages.text: What is the proof that the total number of subsets of a set is $2^n$?
negative_passages.docid: 85817
negative_passages.text: Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
negative_passages.docid: 139078
negative_passages.text: Infinite partition of $\mathbb N$ by infinite subsets
negative_passages.docid: 25834
negative_passages.text: Proof a set cannot contain its own powerset - Russell's Paradox
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 28391
negative_passages.text: Prove the compactness of a set B
negative_passages.docid: 112084
negative_passages.text: Proof of a formula for the power set of a union of two sets
negative_passages.docid: 144787
negative_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 6291
negative_passages.text: Proving something is a linearly independent subset
negative_passages.docid: 71133
negative_passages.text: prove inequlity about cardinality power sets
negative_passages.docid: 113980
negative_passages.text: Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product
negative_passages.docid: 92784
negative_passages.text: Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
negative_passages.docid: 25338
negative_passages.text: Sum of $n$ integers from set of size $2n-1$ divides $n$
negative_passages.docid: 10472
negative_passages.text: Is every set a subset?