A set S is infinite, if and only if S can be put into a one-to-one correspondence with a proper subset of itself
117561
A set is infinite iff there is a one-to-one correspondent with one of its proper subsets?
14512
Why cannot a set be its own element?
66301
The cardinality of the set of countably infinite subsets of an infinite set
97064
Dense set in an infinite cofinite space
58594
Is the empty set a subset of itself?
69838
Does a countably infinite power set exist?
48797
Proving Two Sets are Equal - Infinite Sets - Example
108922
Cardinality and infinite sets: naturals, integers, rationals, bijections
3636
Are any two uncountable sets similar to each other?
152382
Can an infinite set A be larger than an infinite set B but still have the same cardinality?
63276
Is an arbitrary union of a chain of countable sets countable?
112910
Is the set of real numbers really uncountably infinite?
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
132025
Is there an alternative to Cantor's cardinalities that makes proper subsets smaller than their sets?
12436
The cardinality of the set of all finite subsets of an infinite set
107614
Partitioning an infinite set
20140
Example of set which contains itself