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Liouville number

A transcendental number that can be approximated very closely by a rational number. Normally, proving that any given number is transcendental is difficult. However, the French mathematician Joseph Liouville (18091882) showed the existence of a large (in fact, infinitely large) class of transcendentals whose nature is easy to ascertain. A typical Liouville number is 0.101 001 000 000 100 000 000 000 000 000 000 000 01... in which the successive groups of zeros are of length 1!, 2!, 3!, 4!, and so on.

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