Cardinals

Concepts

• Finite set 10 exercisesA set A is finite if there is a bijection between A and \1,dots,n\ for some n∈ℕ, where \1,dots,0\=∅.
• Infinite set 10 exercisesA set A is infinite if it is not finite, that is, if there is no bijection between A and \1,dots,n\ for any n∈ℕ.
• Equipotence 10 exercisesTwo sets A and B are equipotent if there is a bijection fcolon A→ B. It is written Asim B.
• Countable set 10 exercisesA set is countable if it is finite or equipotent to ℕ, that is, if its elements can be listed in a sequence.
• Cantor's diagonal theorem 10 exercisesTheorem proving that the set \0,1\^ℕ of binary sequences is not countable, by building a sequence that appears in no list.
• Cardinal number 10 exercisesThe cardinal number of a set A is the least ordinal equinumerous with A. It measures the size of A and also works for infinite se…
• Schröder–Bernstein theorem 10 exercisesThe Schröder-Bernstein theorem states that if there are injections from A into B and from B into A, then there is a bijection bet…