query: Problem with the number of the elements of a set and its proper subset
positive_passages.docid: 152382
positive_passages.text: Can an infinite set A be larger than an infinite set B but still have the same cardinality?
negative_passages.docid: 147013
negative_passages.text: Subset of a finite set is finite
negative_passages.docid: 107010
negative_passages.text: How many elements of order $k$ are in $S_n$?
negative_passages.docid: 140668
negative_passages.text: Union of $2$ set $A, B$ where $ A$ is a subset of $B$
negative_passages.docid: 72440
negative_passages.text: Partition a set into $k$ non-empty subsets
negative_passages.docid: 17212
negative_passages.text: The preimage of a subset
negative_passages.docid: 91485
negative_passages.text: Finding an uncountable chain of subsets the integers
negative_passages.docid: 98850
negative_passages.text: A positional number system for enumerating fixed-size subsets?
negative_passages.docid: 35362
negative_passages.text: Number of equivalence relations on a set
negative_passages.docid: 1409
negative_passages.text: Proving that the given set has at most $2^{n-1}$ elements
negative_passages.docid: 42603
negative_passages.text: How can I prove that the cadinality of a set minus a finite number of elements of it is still the same as the original set?
negative_passages.docid: 65978
negative_passages.text: How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
negative_passages.docid: 135743
negative_passages.text: Collection of subset generating every pairs of elements
negative_passages.docid: 88628
negative_passages.text: Proving the total number of subsets of S is equal to $2^n$
negative_passages.docid: 153072
negative_passages.text: Guessing a subset of $\{1,...,N\}$
negative_passages.docid: 114968
negative_passages.text: Partition of a set, definition not clear
negative_passages.docid: 69833
negative_passages.text: Number of elements not equal to their inverses is even number