Center of interval belongs to interval How can I prove that
$$ \frac{a+b} {2}\in [a , b], \quad a<b, \quad(a, b) \in \mathbb{R}^2 $$
Thank you, 
Tom

$$a<b\Rightarrow a+a<a+b\Rightarrow 2a<a+b\Rightarrow a<\frac{a+b}{2}$$
Similarly
$$a<b\Rightarrow a+b<b+b\Rightarrow a+b<2b\Rightarrow\frac{a+b}{2}<b$$
So,
$$\frac{a+b}{2}\in\left[a,b\right]$$
