Talk:Transcendental number

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This is annoying me: This and other "Liouville numbers" are artificial examples, rather than numbers that directs our attention to it in a natural way. The first important number --- an eminently "natural" example ---. Are "artificial" transcendental numbers less important than so called "natural" ones? I think not. Just think on Lioville's discovery. I guess the first ones who thought about transcendentality of numbers were Johann Heinrich Lambert and Adrien-Marie Legendre in late 18th century. In the beginning of 19th century all mathematicians have agreed that their hypotheses are correct. Liouville gave a final step, regardless of non-naturality of his numbers. It is the idea that counts. Best regards. --XJam 23:18 Dec 23, 2002 (UTC)

I'm not even sure the "artificial" / "natural" distinction makes sense. The Liouville number seems constructed -- but so is e, if you define it as a summation. Even its definition as the base of natural log is artificial -- we've defined it as "the number that is the base of natural log". Why is that more natural than "the number whose nth digit is 1 if n is ... bla bla" ? -- Tarquin 23:24 Dec 23, 2002 (UTC)

Yes, why? :-) Perhaps π is the most "natural" as the other numbers... Perhaps. --XJamRastafire 23:36 Dec 23, 2002 (UTC)

I have a feeling that besides pi and e, the original author would be hard pressed to give an example of a "natural" number which is transcendental - since there doesn't seem to be an obvious sense of what "natural" is supposed to imply here - constructible? computable? commonly used? "useful"? or what? If I read the article a few more times, I'm sure it will irk me enough to "boldy edit" the distinction out of existence. Chas zzz brown 00:46 Dec 24, 2002 (UTC)