How do you call real numbers that are not part of any solution of finite set of any type of equations that consists...

>Oh sorry i thought your image said R -Q = {?} and didn't bother to read your question thoroughly.
OP here: pic is not related

solution for thist is transcendental, so youre wrong

Transcendental numbers and the roots of Polynomials with Integer coefficients.

Or the empty set if you ask Wildberger, lol

You're getting on shaky territory. You can't define
a 'definable number'
>en.wikipedia.org/wiki/Tarski's_undefinability_theorem
Anyway, look up descriptive set theory if you're interested in that kind of stuff.

>Transcendental numbers and the roots of Polynomials with Integer coefficients.
find me and equasion that solution is 1.01100111000111100001111100000111111...

Non computable numbers.

OP here:
Transcendental? NO. Proof: 2^2^(1/2)

That solution is a real therefore there is an integer coefficient equation that has it has a root.
QED

>Non computable numbers
thanks user
>en.wikipedia.org/wiki/Chaitin's_constant

but, is there a number that cannot be defined as non computable nor computable number and its real?

What you're talking about is somewhere between transcendental and nondefinable. It depends on what kind of equations you use.

are you really asking if there is something that is neither X nor not X?

>equations that consists only rational numbers
you have e in your equation

You usually use some formal representation of algorithms. church's thesis asserts they are all equivalent

u can replace it by 3 and we're good.