Transcendental

• $\pi$ is transcendental.

• $(1-\pi)$ is transcendental.

$\pi +(1-\pi) = 1$

Where 1 is not a transcendental number.

Hence the answer is $\color{#D61F06} \boxed{\text{false}}$

$e \text { is transcendental }$ .

$\text { And } 1 - e \text { is also transcendental }$ .

$e + 1 - e = 1 \text { is not transcendental }$ .

Let L/K be an algebraic field extension and M/L be a transcendent one.

Then take l∈L and m∈M

Then we (l+m)+(−m)=l which is algebraic.

(m+l) is transcendent because L is closed.

This is not different for the field extensions

A/Q and R/A

where the first one is algebraic and the 2nd one is transcendental.