Re: Transcendent Numbers: TO WHAT are they transcendent??

On Sep 19, 10:55 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1190260361.339593.89...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
finite guy <adamle...@xxxxxxxxxxxx> wrote:

Transcendent Numbers: TO WHAT are they transcendent??

They transcend polynomial equations with integer coefficients, which
algebraic numbers do not.

I.e., every algebraic number is a solution to such an equation, but
transcendental numbers are not.

Possibly dumb question: are there other classes defined by still-
higher
order operations?

The inverse of addition on the naturals gives rise to the integers.
The inverse of multiplication on the integers gives rise to the
rationals.
The inverse of exponentation on the rationals gives rise to the
algebraic numbers.
Does the inverse of tetration give rise to another class of numbers
that
are not algebraic but are still computable?

Is there an infinite series of these classes of numbers? Does the
union
of all of these classes form the computable numbers?


Marshall

.

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