How do you call real numbers that are not part of any solution

>>8306941
Irrational numbers?

>>8306941
irrational numbers.

Transcendental?

>>8306941
like thist 0.10110011100011110000...

>>8306949
x^(1/2)=e^x

>>8306947
x=2^(1/2)

>>8306949
the transcendentals are included in the irrationals, but not vice versa. Consider sqrt(2).

>>8306962
yeah, but the transcendentals are not the right set

Oh sorry i thought your image said R -Q = {?} and didn't bother to read your question thoroughly.

>>8306949
This is correct

>>8306941
>Oh sorry i thought your image said R -Q = {?} and didn't bother to read your question thoroughly.
OP here: pic is not related

>>8306967
solution for thist >>8306954 is transcendental, so youre wrong

>>8306941
Transcendental numbers and the roots of Polynomials with Integer coefficients.

Or the empty set if you ask Wildberger, lol

>>8306941
You're getting on shaky territory. You can't define
a 'definable number'
>https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem
Anyway, look up descriptive set theory if you're interested in that kind of stuff.

>>8306989
>Transcendental numbers and the roots of Polynomials with Integer coefficients.
find me and equasion that solution is 1.01100111000111100001111100000111111...

>>8306941
Non computable numbers.

>>8306941
OP here:
Transcendental? NO. Proof: 2^2^(1/2)

>>8307000
That solution is a real therefore there is an integer coefficient equation that has it has a root.
QED

>>8307006
>Non computable numbers
thanks anon
>https://en.wikipedia.org/wiki/Chaitin%27s_constant

>>8307006
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.

>>8307026
are you really asking if there is something that is neither X nor not X?

>>8306954
>equations that consists only rational numbers
you have e in your equation

>>8307045
You usually use some formal representation of algorithms. church's thesis asserts they are all equivalent

>>8307053
u can replace it by 3 and we're good.