Page 192 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

such that each x n is either 0 or 1, but

∞
{x n } n=1 / ∈ S.

By the definition of S , this will be a contradiction. Since we want the sequence

∞
{x n } n=1

to be different from the sequence s 1 , let’s define

x 1 =1 if thefirstelement of s 1 is 0,

x 1 =0 if thefirstelement of s 1 is 1.

This ensures that the sequence is not the same as s 1 , because its first element is different. So, let’s do the
same thing for the second element,

x 2 =1 if thesecond elementof s 2 is 0,

x 2 =0 if thesecond elementof s 2 is 1.

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