What is an irrational number?
Irrational number
It is not known if 



π
+
e


{\displaystyle \pi +e}

 (or 



π
−
e


{\displaystyle \pi -e}

) is irrational. In fact, there is no pair of non-zero integers 



m
,
n


{\displaystyle m,n}

 for which it is known whether 



m
π
+
n
e


{\displaystyle m\pi +ne}

 is irrational. Moreover, it is not known whether or not the set 



{
π
,
e
}


{\displaystyle \{\pi ,e\}}

 is algebraically independent over 




Q



{\displaystyle \mathbb {Q} }

.