819 名前：pload.wikimedia.org/wikipedia/commons/thumb/b/b7/Diagonal_argument_01_svg.svg/375px-Diagonal_argument_01_svg.svg.png An illustration of Cantor's diagonal argument (in base 2) for the existence of uncountable sets. The sequence at the bottom cannot occur anywhere in the enumeration of sequences above.
Uncountable set Cantor considered the set T of all infinite sequences of binary digits (i.e. each digit is zero or one).[note 2] He begins with a constructive proof of the following lemma:
If s1, s2, ... , sn, ... is any enumeration of elements from T,[note 3] then an element s of T can be constructed that doesn't correspond to any sn in the enumeration. The proof starts with an enumeration of elements from T, for example s1 =(0,0,0,0,0,0,0,...) s2 =(1,1,1,1,1,1,1,...) s3 =(0,1,0,1,0,1,0,...) s4 =(1,0,1,0,1,0,1,...) s5 =(1,1,0,1,0,1,1,...) s6 =(0,0,1,1,0,1,1,...) s7 =(1,0,0,0,1,0,0,...) ... (引用終り) 以上 []
