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Preamble; the switching map
Preamble; the switching map
, the maps
and
Injections into
Surjections from
Definition of finiteness
The Pigeonhole Principle, injective version
The Pigeonhole Principle, surjective version
The number of elements of a finite set is unique
Criteria for finiteness of a set
Countable sets
Cantor's Power Set Theorem; uncountable sets
A surjection:
; the reals are uncountable
Cantor's Bijection Theorem
Relations: partial orders, equivalences
The equivalence relation of an injection
The proof of Cantor's Bijection Theorem, using equivalence relations
About this document ...
George A. J. Sparling 2012-02-09
, the maps 
and
![$ \mathcal{P}(\mathbb{N}) \rightarrow [0, 1]$](img290.png){kind=small}
; the reals are uncountable